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Hustle Calculus

Test #643

Hustle Calculus

Test #643

Hustle Calculus

Test #643

Hustle Calculus

Test #643

#1 Calculus – Hustle MAΘ National Convention 2018

#1 Calculus – Hustle MAΘ National Convention 2018

Evaluate 0

sin 4limx

x

x→

.

Evaluate 0

sin 4limx

x

x→

.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#1 Calculus – Hustle MAΘ National Convention 2018

#1 Calculus – Hustle MAΘ National Convention 2018

Evaluate 0

sin 4limx

x

x→

.

Evaluate 0

sin 4limx

x

x→

.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#2 Calculus – Hustle MAΘ National Convention 2018

#2 Calculus – Hustle MAΘ National Convention 2018

Evaluate ( )

0

ln 1limx

x

x→

+

.

Evaluate ( )

0

ln 1limx

x

x→

+

.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#2 Calculus – Hustle MAΘ National Convention 2018

#2 Calculus – Hustle MAΘ National Convention 2018

Evaluate ( )

0

ln 1limx

x

x→

+

.

Evaluate ( )

0

ln 1limx

x

x→

+

.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#3 Calculus – Hustle MAΘ National Convention 2018

#3 Calculus – Hustle MAΘ National Convention 2018

Find dy

dx if

2x

x

xe xy

x e

−=

+.

Find dy

dx if

2x

x

xe xy

x e

−=

+.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#3 Calculus – Hustle MAΘ National Convention 2018

#3 Calculus – Hustle MAΘ National Convention 2018

Find dy

dx if

2x

x

xe xy

x e

−=

+.

Find dy

dx if

2x

x

xe xy

x e

−=

+.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#4 Calculus – Hustle MAΘ National Convention 2018

#4 Calculus – Hustle MAΘ National Convention 2018

Find dy

dx if ln tany x= .

Find dy

dx if ln tany x= .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#4 Calculus – Hustle MAΘ National Convention 2018

#4 Calculus – Hustle MAΘ National Convention 2018

Find dy

dx if ln tany x= .

Find dy

dx if ln tany x= .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#5 Calculus – Hustle MAΘ National Convention 2018

#5 Calculus – Hustle MAΘ National Convention 2018 At what point(s) of the ellipse 2 216 9 400x y+ =

does the ordinate decrease at the same rate as the abscissa increases?

At what point(s) of the ellipse 2 216 9 400x y+ =

does the ordinate decrease at the same rate as the abscissa increases?

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#5 Calculus – Hustle MAΘ National Convention 2018

#5 Calculus – Hustle MAΘ National Convention 2018 At what point(s) of the ellipse 2 216 9 400x y+ =

does the ordinate decrease at the same rate as the abscissa increases?

At what point(s) of the ellipse 2 216 9 400x y+ =

does the ordinate decrease at the same rate as the abscissa increases?

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#6 Calculus – Hustle MAΘ National Convention 2018

#6 Calculus – Hustle MAΘ National Convention 2018 The distance d that an image is from a certain

lens in terms of c, the distance the object is

from the lens, is given by 10

10

cd

c=

−. If the

object distance is increasing at the rate of 0.2 cm/sec, how fast is the image distance changing when 15c = cm?

The distance d that an image is from a certain lens in terms of c, the distance the object is

from the lens, is given by 10

10

cd

c=

−. If the

object distance is increasing at the rate of 0.2 cm/sec, how fast is the image distance changing when 15c = cm?

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#6 Calculus – Hustle MAΘ National Convention 2018

#6 Calculus – Hustle MAΘ National Convention 2018 The distance d that an image is from a certain

lens in terms of c, the distance the object is

from the lens, is given by 10

10

cd

c=

−. If the

object distance is increasing at the rate of 0.2 cm/sec, how fast is the image distance changing when 15c = cm?

The distance d that an image is from a certain lens in terms of c, the distance the object is

from the lens, is given by 10

10

cd

c=

−. If the

object distance is increasing at the rate of 0.2 cm/sec, how fast is the image distance changing when 15c = cm?

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#7 Calculus – Hustle MAΘ National Convention 2018

#7 Calculus – Hustle MAΘ National Convention 2018 Find the equation of a normal line to the curve

lny x x= that is parallel to the straight line

2 2 3 0x y− + = .

Find the equation of a normal line to the curve lny x x= that is parallel to the straight line

2 2 3 0x y− + = .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#7 Calculus – Hustle MAΘ National Convention 2018

#7 Calculus – Hustle MAΘ National Convention 2018 Find the equation of a normal line to the curve

lny x x= that is parallel to the straight line

2 2 3 0x y− + = .

Find the equation of a normal line to the curve lny x x= that is parallel to the straight line

2 2 3 0x y− + = .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#8 Calculus – Hustle MAΘ National Convention 2018

#8 Calculus – Hustle MAΘ National Convention 2018

Evaluate ( )

23

dx

b ax+ .

Evaluate ( )

23

dx

b ax+ .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#8 Calculus – Hustle MA National Convention 2018

#8 Calculus – Hustle MAΘ National Convention 2018

Evaluate ( )

23

dx

b ax+ .

Evaluate ( )

23

dx

b ax+ .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#9 Calculus – Hustle MAΘ National Convention 2018

#9 Calculus – Hustle MAΘ National Convention 2018

Evaluate ( )

2

2 2

1 2

1

xdx

x x

+

+ .

Evaluate ( )

2

2 2

1 2

1

xdx

x x

+

+ .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#9 Calculus – Hustle MAΘ National Convention 2018

#9 Calculus – Hustle MAΘ National Convention 2018

Evaluate ( )

2

2 2

1 2

1

xdx

x x

+

+ .

Evaluate ( )

2

2 2

1 2

1

xdx

x x

+

+ .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#10 Calculus – Hustle MAΘ National Convention 2018

#10 Calculus – Hustle MAΘ National Convention 2018

Evaluate 25 2 3

2

x xdx

x

+ −

+ .

Evaluate 25 2 3

2

x xdx

x

+ −

+ .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#10 Calculus – Hustle MAΘ National Convention 2018

#10 Calculus – Hustle MAΘ National Convention 2018

Evaluate 25 2 3

2

x xdx

x

+ −

+ .

Evaluate 25 2 3

2

x xdx

x

+ −

+ .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#11 Calculus – Hustle MAΘ National Convention 2018

#11 Calculus – Hustle MAΘ National Convention 2018

Evaluate

2

2

5

3 1

xd

t t dtdx

+ + .

Evaluate

2

2

5

3 1

xd

t t dtdx

+ + .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#11 Calculus – Hustle MAΘ National Convention 2018

#11 Calculus – Hustle MAΘ National Convention 2018

Evaluate

2

2

5

3 1

xd

t t dtdx

+ + .

Evaluate

2

2

5

3 1

xd

t t dtdx

+ + .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#12 Calculus – Hustle MAΘ National Convention 2018

#12 Calculus – Hustle MAΘ National Convention 2018 Evaluate cosxe xdx . Evaluate cosxe xdx .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#12 Calculus – Hustle MAΘ National Convention 2018

#12 Calculus – Hustle MAΘ National Convention 2018 Evaluate cosxe xdx . Evaluate cosxe xdx .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#13 Calculus – Hustle MAΘ National Convention 2018

#13 Calculus – Hustle MAΘ National Convention 2018

Evaluate 2

2 34

3 11 4

xdx

x x

− − .

Evaluate 2

2 34

3 11 4

xdx

x x

− − .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#13 Calculus – Hustle MAΘ National Convention 2018

#13 Calculus – Hustle MAΘ National Convention 2018

Evaluate 2

2 34

3 11 4

xdx

x x

− − .

Evaluate 2

2 34

3 11 4

xdx

x x

− − .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#14 Calculus – Hustle MAΘ National Convention 2018

#14 Calculus – Hustle MAΘ National Convention 2018

Evaluate 2 2

a

a

dx

a x− − .

Evaluate 2 2

a

a

dx

a x− − .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#14 Calculus – Hustle MAΘ National Convention 2018

#14 Calculus – Hustle MAΘ National Convention 2018

Evaluate 2 2

a

a

dx

a x− − .

Evaluate 2 2

a

a

dx

a x− − .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#15 Calculus – Hustle MAΘ National Convention 2018

#15 Calculus – Hustle MAΘ National Convention 2018 Let ( )g x be the inverse of ( )f x . The selected

values of ( )f x and ( )'f x are given in the

table below. Find the value of ( )' 5g .

x 0 2 5

( )f x 8 5 3

( )'f x 7 1 4

Let ( )g x be the inverse of ( )f x . The selected

values of ( )f x and ( )'f x are given in the

table below. Find the value of ( )' 5g .

x 0 2 5

( )f x 8 5 3

( )'f x 7 1 4

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#15 Calculus – Hustle MA National Convention 2018

#15 Calculus – Hustle MAΘ National Convention 2018 Let ( )g x be the inverse of ( )f x . The selected

values of ( )f x and ( )'f x are given in the

table below. Find the value of ( )' 5g .

x 0 2 5

( )f x 8 5 3

( )'f x 7 1 4

Let ( )g x be the inverse of ( )f x . The selected

values of ( )f x and ( )'f x are given in the

table below. Find the value of ( )' 5g .

x 0 2 5

( )f x 8 5 3

( )'f x 7 1 4

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#16 Calculus – Hustle MAΘ National Convention 2018

#16 Calculus – Hustle MAΘ National Convention 2018 Find any real values of x for which the

derivative of 2

2 1

xy

x=

+ is zero.

Find any real values of x for which the

derivative of 2

2 1

xy

x=

+ is zero.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#16 Calculus – Hustle MAΘ National Convention 2018

#16 Calculus – Hustle MAΘ National Convention 2018 Find any real values of x for which the

derivative of 2

2 1

xy

x=

+ is zero.

Find any real values of x for which the

derivative of 2

2 1

xy

x=

+ is zero.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#17 Calculus – Hustle MAΘ National Convention 2018

#17 Calculus – Hustle MAΘ National Convention 2018 Find the y-intercept of the line normal to the

curve 33y x x= − at ( )3, 18− .

Find the y-intercept of the line normal to the

curve 33y x x= − at ( )3, 18− .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#17 Calculus – Hustle MAΘ National Convention 2018

#17 Calculus – Hustle MAΘ National Convention 2018 Find the y-intercept of the line normal to the

curve 33y x x= − at ( )3, 18− .

Find the y-intercept of the line normal to the

curve 33y x x= − at ( )3, 18− .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#18 Calculus – Hustle MAΘ National Convention 2018

#18 Calculus – Hustle MAΘ National Convention 2018 The illuminance I, which is positive, at a point

is inversely proportional to the square of the distance x from the source. Find

0limx

I→

.

The illuminance I, which is positive, at a point is inversely proportional to the square of the distance x from the source. Find

0limx

I→

.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#18 Calculus – Hustle MAΘ National Convention 2018

#18 Calculus – Hustle MAΘ National Convention 2018 The illuminance I, which is positive, at a point

is inversely proportional to the square of the distance x from the source. Find

0limx

I→

.

The illuminance I, which is positive, at a point is inversely proportional to the square of the distance x from the source. Find

0limx

I→

.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#19 Calculus – Hustle MAΘ National Convention 2018

#19 Calculus – Hustle MAΘ National Convention 2018 The strength of a rectangular beam is

proportional to the product of its width and the square of its depth. Find the dimensions, in inches, of the strongest beam that can be cut from a circular log 16 inches in diameter.

The strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions, in inches, of the strongest beam that can be cut from a circular log 16 inches in diameter.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#19 Calculus – Hustle MAΘ National Convention 2018

#19 Calculus – Hustle MAΘ National Convention 2018 The strength of a rectangular beam is

proportional to the product of its width and the square of its depth. Find the dimensions, in inches, of the strongest beam that can be cut from a circular log 16 inches in diameter.

The strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions, in inches, of the strongest beam that can be cut from a circular log 16 inches in diameter.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#20 Calculus – Hustle MAΘ National Convention 2018

#20 Calculus – Hustle MAΘ National Convention 2018 Let ( ) 2f x x x= − and ( )g x ax= . Determine a

so that the region above the graph of g and

below the graph of f has area 9

2.

Let ( ) 2f x x x= − and ( )g x ax= . Determine a

so that the region above the graph of g and

below the graph of f has area 9

2.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#20 Calculus – Hustle MAΘ National Convention 2018

#20 Calculus – Hustle MAΘ National Convention 2018 Let ( ) 2f x x x= − and ( )g x ax= . Determine a

so that the region above the graph of g and

below the graph of f has area 9

2.

Let ( ) 2f x x x= − and ( )g x ax= . Determine a

so that the region above the graph of g and

below the graph of f has area 9

2.

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#21 Calculus – Hustle MAΘ National Convention 2018

#21 Calculus – Hustle MAΘ National Convention 2018 Determine the derivative ( )'f x of

( ) ( )sin sin sinf x x = .

Determine the derivative ( )'f x of

( ) ( )sin sin sinf x x = .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#21 Calculus – Hustle MAΘ National Convention 2018

#21 Calculus – Hustle MAΘ National Convention 2018 Determine the derivative ( )'f x of

( ) ( )sin sin sinf x x = .

Determine the derivative ( )'f x of

( ) ( )sin sin sinf x x = .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#22 Calculus – Hustle MAΘ National Convention 2018

#22 Calculus – Hustle MAΘ National Convention 2018 Determine the derivative ( )'f x of

( )2

2

sin

sin

xf x

x= .

Determine the derivative ( )'f x of

( )2

2

sin

sin

xf x

x= .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#22 Calculus – Hustle MA National Convention 2018

#22 Calculus – Hustle MAΘ National Convention 2018 Determine the derivative ( )'f x of

( )2

2

sin

sin

xf x

x= .

Determine the derivative ( )'f x of

( )2

2

sin

sin

xf x

x= .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#23 Calculus – Hustle MAΘ National Convention 2018

#23 Calculus – Hustle MAΘ National Convention 2018 Find the average value of ( ) 22 3 3f x x x= + + in

the interval [1,4].

Find the average value of ( ) 22 3 3f x x x= + + in

the interval [1,4].

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#23 Calculus – Hustle MAΘ National Convention 2018

#23 Calculus – Hustle MAΘ National Convention 2018 Find the average value of ( ) 22 3 3f x x x= + + in

the interval [1,4].

Find the average value of ( ) 22 3 3f x x x= + + in

the interval [1,4].

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#24 Calculus – Hustle MAΘ National Convention 2018

#24 Calculus – Hustle MAΘ National Convention 2018 Find the volume of the solid generated by

revolving about the x-axis the area bounded by

the parabolas 2 28 and 8y x y x= = .

Find the volume of the solid generated by revolving about the x-axis the area bounded by

the parabolas 2 28 and 8y x y x= = .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#24 Calculus – Hustle MAΘ National Convention 2018

#24 Calculus – Hustle MAΘ National Convention 2018 Find the volume of the solid generated by

revolving about the x-axis the area bounded by

the parabolas 2 28 and 8y x y x= = .

Find the volume of the solid generated by revolving about the x-axis the area bounded by

the parabolas 2 28 and 8y x y x= = .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#25 Calculus – Hustle MAΘ National Convention 2018

#25 Calculus – Hustle MAΘ National Convention 2018

Solve for y if 5 2

7

dy x

dx y

+= , 𝑦 > 0, and

1 when 2y x= = .

Solve for y if

5 2

7

dy x

dx y

+= , 𝑦 > 0, and

1 when 2y x= = .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5

#25 Calculus – Hustle MAΘ National Convention 2018

#25 Calculus – Hustle MAΘ National Convention 2018

Solve for y if 5 2

7

dy x

dx y

+= , 𝑦 > 0, and

1 when 2y x= = .

Solve for y if

5 2

7

dy x

dx y

+= , 𝑦 > 0, and

1 when 2y x= = .

Answer : ________________________ Round 1 2 3 4 5

Answer : ________________________ Round 1 2 3 4 5