Exam (elaborations) MTH 112

ND1 Calculus Past Question Practice Booklet

Page 1: Calculus Problem Set


Question 1:

Find the derivative of f(x) = 3x^3 - 5x^2 + 2x - 7



Solution:

f'(x) = d/dx(3x^3 - 5x^2 + 2x - 7)

= 9x^2 - 10x + 2



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Question 2:

Evaluate the integral of (4x^3 - 2x + 1) dx



Solution:

Integral = x^4 - x^2 + x + C



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Question 3:

If y = e^(2x), find dy/dx



Solution:

dy/dx = 2e^(2x)



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Question 4:

Find the limit: lim x->2 of (x^2 - 4)/(x - 2)



Solution:

= ((x-2)(x+2))/(x-2) = x + 2


Page 1

, ND1 Calculus Past Question Practice Booklet

As x approaches 2, limit = 4




Page 2

, ND1 Calculus Past Question Practice Booklet

Page 2: Calculus Problem Set


Question 1:

Find the derivative of f(x) = 3x^3 - 5x^2 + 2x - 7



Solution:

f'(x) = d/dx(3x^3 - 5x^2 + 2x - 7)

= 9x^2 - 10x + 2



---



Question 2:

Evaluate the integral of (4x^3 - 2x + 1) dx



Solution:

Integral = x^4 - x^2 + x + C



---



Question 3:

If y = e^(2x), find dy/dx



Solution:

dy/dx = 2e^(2x)



---



Question 4:

Find the limit: lim x->2 of (x^2 - 4)/(x - 2)



Solution:

= ((x-2)(x+2))/(x-2) = x + 2


Page 3

, ND1 Calculus Past Question Practice Booklet

As x approaches 2, limit = 4




Page 4