## Jul 18, 2009

### Differential and Integral Calculus - Multiple Choice Questions - Part II

1. What is the primary difference between using anti-differentiation when finding a definite versus an indefinite integral?

Indefinite integrals don't have defined limits.

Definite integrals have defined limits.

The constant of integration, C.

There is no difference between definite and indefinite integrals.

2. If θ approaches zero, then limit of sin(θ)/θ is _____.

cos(θ)

0

1

This is indeterminate.

3. Let's say that f ''(k) = 0 @ (13, -2). What does this mean?

There is definitely an inflection point at that location.

There might be an inflection point at that location.

There definitely is not an inflection point at that location.

There's no way to tell without first knowing what the specific function is.

4. What is the one thing done in anti-differentiation that has no counterpart in differentiation?

Subtracting a constant C.

Dividing the new exponent by a constant C.

Nothing, they are equally matched step by step.

5. What is a necessary condition for L'Hôpital's Rule to work?

The function must be determinate.

The function must be indeterminate.

The function must be inconsistent.

The function must possess at least three non-zero derivatives.

6. What does du equal in ∫2x(x2 + 1)5 dx?

2x

2u du

2x dx

5u4

7. What is the second step of performing anti-differentiation?

Divide the coefficient by the old exponential value.

Subtract the new exponential value from the coefficient.

Multiply the coefficient by the new exponential value.

Divide the coefficient by the new exponential value.

8. Which of the following is the best integration technique to use for ∫2x(x2 + 1)5 dx?

The product rule.

The chain rule.

The power rule.

The substitution rule.

9. ∫1/x dx =

Undefined because you cannot divide by zero.

loge(x)

ln(x)

ln(x) + C

10. What is the converted substitution form of ∫12x2 (x3 + 1)5 dx?

4∫u5 du

∫u5 du

¼ ∫u5 du

This cannot be solved by the substitution method.