Calculus: Limits & Derivatives

Question 1

What is the derivative of x²?

A x B 2x C x³ D 2

💡 Explanation

2x is correct because by the power rule, d/dx(xⁿ) = n·xⁿ⁻¹, so d/dx(x²) = 2x.

Question 2

The derivative of a constant is:

A The constant itself B 1 C 0 D Undefined

💡 Explanation

0 is correct because a constant does not change, so its rate of change is zero.

Question 3

What does the derivative of a function represent?

A Area under the curve B Instantaneous rate of change C Total distance D The y-intercept

💡 Explanation

Instantaneous rate of change is correct because the derivative gives the slope of the tangent at a point.

Question 4

Evaluate the limit of (x) as x approaches 5.

A 0 B 1 C 5 D Undefined

💡 Explanation

5 is correct because the function f(x) = x is continuous, so the limit equals 5.

Question 5

The derivative of 3x is:

A 3 B x C 3x D 0

💡 Explanation

3 is correct because the derivative of a linear term ax is the constant a.