Adaptive Practice
Limits and Derivatives
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Question 1 of 10
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Easy
Evaluate \( \lim_{x \to 2} \frac{x^2 - 4}{x - 2} \).
Easy
If \( f(x) = 3x^3 - 5x + 2 \), find \( f'(x) \).
Easy
Find \( \lim_{x \to 0} \frac{\sin 3x}{x} \).
Easy
If \( y = \sqrt{x} \), find \( \frac{dy}{dx} \).
Medium
Evaluate \( \lim_{x \to 1} \frac{x^3 - 1}{x - 1} \).
Medium
If \( f(x) = \frac{1}{x} \), find \( f'(x) \).
Medium
Find the derivative of \( f(x) = x \sin x \).
Medium
Evaluate \( \lim_{x \to 0} \frac{e^x - 1}{x} \).
Hard
Find \( \frac{d}{dx} \left( \frac{x^2 + 1}{x} \right) \).
Hard
If \( y = \ln(\sin x) \), find \( \frac{dy}{dx} \).