7/31/2019 Scheme(Assignment 4)

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Since P(20) > 0, profit is increasing at this level of production

Question 2:

H(t) = 4.4t4.9t2

a. H(t) = 4.49.8t

the rate at which H(t) is changing after 1 second

H(1) = 4.49.8(1) = 5.4

since H(1)

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y(x) = m

Question 4:

f(x) =

x i f x 0

x i f x < 0

when x 0

f(x) = limh0f(x+h)f(x)

h= limh0{

(x+h)xh

}= limh0(hh

) = 1

when x < 0

f(x) = limh0{(x+h)(x)

h}= limh0(

hh

) = 1

hence

f(x) =

1 x 0

1 < 0

Question 5:

a. By definition

f(c) = limh0(f(c+h)f(c)

h)

let h = x cx = h + c

Then as h 0,x c

f(c) = limxc(f(c+xc)f(c)

xc ) =f(x)f(c)

xc

hence f(c) =f(x)f(c)

xc

b. f(x) f(c) = [f(x)f(c)

xc ](xc)

limxc[f(x) f(c)] = limxc[f(x)f(c)

xc ](x c)

= limxc[f(x)f(c)

xc ]. limxc(x c)

limxc(x c) = 0 and

limxc[f(x)f(c)

xc ] = f(c)

limxc[f(x) f(c)] = f(c).0

hence

limxc[f(x) f(c)] = 0

c. limxc[f(x) f(c)] = 0

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