Limits and Derivatives

The derivative of xⁿ is:

1. nxⁿ
2. n xⁿ⁻¹
3. xⁿ⁻¹
4. nⁿx

If f(x) = x³, then f'(2) is:

1. 4
2. 6
3. 12
4. 8

The value of lim x→0 (aˣ − 1)/x is:

1. 0
2. 1
3. log a
4. a

The derivative of cos x is:

1. sin x
2. −sin x
3. cos x
4. −cos x

A function is continuous at x = a if:

1. Limit exists and equals f(a)
2. Limit is zero
3. Derivative is zero
4. Function is constant

The derivative of log x is:

1. x
2. 1/x
3. log x
4. eˣ

The value of lim x→0 (tan x)/x is:

1. 0
2. 1
3. ∞
4. −1

If y = 3x³ + 5x, then dy/dx is:

1. 9x² + 5
2. 3x² + 5
3. 9x³ + 5
4. 6x + 5

The derivative of eˣ is:

1. xeˣ
2. eˣ
3. log x
4. 1/eˣ

The value of lim x→a (x² − a²)/(x − a) is:

1. a
2. 2a
3. a²
4. 0

The derivative of sin x is:

1. cos x
2. −sin x
3. −cos x
4. tan x

The derivative of a constant function is:

1. 1
2. Constant itself
3. 0
4. Undefined

If f(x) = x², then f'(x) is:

1. x
2. 2x
3. x²
4. 2

The value of lim x→0 (1 − cos x)/x² is:

1. 0
2. 1
3. 1/2
4. 2

The value of lim x→0 (sin x)/x is:

1. 0
2. 1
3. ∞
4. Does not exist