Hustle - Mu Alpha Thetamualphatheta.org/useruploads/files/conventionfiles/past_tests/Calcul… ·...
of 27
/27
Embed Size (px)
Transcript of Hustle - Mu Alpha Thetamualphatheta.org/useruploads/files/conventionfiles/past_tests/Calcul… ·...
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
