NSAA NSAA Mathematics - Calculus 3

Question 1

The product rule for differentiation states: d/dx[f(x)g(x)] =

Accepted Answer

f'(x)g(x) + f(x)g'(x)

Answer

f'(x)g'(x)

Answer

f'(x)g(x) - f(x)g'(x)

Answer

f(x)/g'(x)

Question 2

Evaluate ∫ sin(x) dx

Accepted Answer

-cos(x) + C

Answer

cos(x) + C

Answer

sin(x) + C

Answer

-sin(x) + C

Question 3

A particle's position is given by s(t) = t³ - 6t. What is the velocity at t = 2?

Accepted Answer

6

Answer

2

Answer

8

Answer

10

Question 4

Find the x-coordinate of the stationary point of y = x² - 6x + 9.

Accepted Answer

x = 3

Answer

x = 0

Answer

x = 6

Answer

x = 9

Question 5

The integral ∫ 1/x dx equals:

Accepted Answer

ln|x| + C

Answer

-1/x² + C

Answer

x + C

Answer

e^x + C

Question 6

Using implicit differentiation, find dy/dx if x² + y² = 25.

Accepted Answer

-x/y

Answer

y/x

Answer

-y/x

Answer

x/y