Adaptive Practice
Limits and Derivatives
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Question 1 of 10
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Easy
Find \( \lim_{x \to 2} \frac{x^2 - 4}{x - 2} \).
Easy
Evaluate \( \lim_{x \to 0} \frac{\sin 3x}{x} \).
Easy
If \(f(x) = x^3 - 5x + 6\), find \(f'(2)\).
Medium
Find \( \lim_{x \to 0} \frac{e^{2x} - 1}{x} \).
Medium
If \(y = \sqrt{1 + \sin x}\), find \(\frac{dy}{dx}\) at \(x = \frac{\pi}{2}\).
Medium
Evaluate \( \lim_{x \to 0} \frac{\tan 5x}{\sin 3x} \).
Hard
Find the derivative of \(f(x) = \frac{x^2 + 1}{x - 1}\).
Hard
Evaluate \( \lim_{x \to 0} \frac{(1 + x)^{\frac{1}{x}} - e}{x} \).
Hard
If \(y = x^x\), find \(\frac{dy}{dx}\).
Medium
Find \( \lim_{x \to 1} \frac{x^{1/3} - 1}{x - 1} \).