alleryThe value of $\displaystyle\lim_{x\to 0}\frac{\sin x}{x}$ is:
- 1
- 0
- $\tfrac{1}{2}$
- $\infty$
Show answer and solution
Correct answer: A. 1
A standard limit: lim_{x→0} (sin x)/x = 1.
AP Intermediate 1st Year Limits and Derivatives — practice questions
Explore 50 free Limits and Derivatives questions in AP Intermediate 1st Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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The value of $\displaystyle\lim_{x\to 0}\frac{\sin x}{x}$ is:Read the answer and worked solution →The derivative of $x^n$ with respect to $x$ is:Read the answer and worked solution →The derivative of a constant function is:Read the answer and worked solution →The value of $\displaystyle\lim_{x\to 2} x^2$ is:Read the answer and worked solution →The derivative of $\sin x$ with respect to $x$ is:Read the answer and worked solution →By first principles, the derivative of $f$ at $x$ is $\displaystyle\lim_{h\to 0}$ of:Read the answer and worked solution →The derivative of $x^3$ with respect to $x$ is:Read the answer and worked solution →The value of $\displaystyle\lim_{x\to 0}\frac{1-\cos x}{x}$ is:Read the answer and worked solution →If $f(x)=x^2+3x$, then $f'(x)$ equals:Read the answer and worked solution →The derivative of $\cos x$ with respect to $x$ is:Read the answer and worked solution →The value of $\displaystyle\lim_{x\to 3}\frac{x^2-9}{x-3}$ is:Read the answer and worked solution →For a constant $c$, $\dfrac{d}{dx}\big(c\,f(x)\big)$ equals:Read the answer and worked solution →The value of $\displaystyle\lim_{x\to 0}\frac{\tan x}{x}$ is:Read the answer and worked solution →The derivative of $\sin x$ is:Read the answer and worked solution →The famous standard limit lim_{x→0} (sin x)/x (with x in radians) equals:Read the answer and worked solution →The expression 0/0 is called:Read the answer and worked solution →Using the QUOTIENT rule, d/dx [f(x)/g(x)] equals:Read the answer and worked solution →Using the CHAIN rule, d/dx [sin(3x)] equals:Read the answer and worked solution →The derivative of the natural logarithm function, d/dx [ln(x)] equals:Read the answer and worked solution →A function f is continuous at x = a if and only if:Read the answer and worked solution →The function f(x) = |x| at x = 0 is:Read the answer and worked solution →The TANGENT line to y = x² at the point (2, 4) has equation:Read the answer and worked solution →Match each limit to its value.Read the answer and worked solution →lim(x→0) (sin x) / x equals:Read the answer and worked solution →If f(x) = x², then f′(x) is:Read the answer and worked solution →d/dx (sin x) is:Read the answer and worked solution →d/dx (cos x) is:Read the answer and worked solution →If f(x) = c (a constant), then f′(x) is:Read the answer and worked solution →lim(x→1) (x² − 1) / (x − 1) equals:Read the answer and worked solution →lim(x→0) (1 − cos x) / x² equals:Read the answer and worked solution →
Worked practice questions
The derivative of $x^n$ with respect to $x$ is:
- $x^{n-1}$
- $n x^{n-1}$
- $\dfrac{x^{n+1}}{n+1}$
- $n x^{n+1}$
Show answer and solution
Correct answer: B. $n x^{n-1}$
Power rule: d/dx(xⁿ) = n x^{n−1}.
The derivative of a constant function is:
- the constant itself
- 1
- 0
- undefined
Show answer and solution
Correct answer: C. 0
A constant does not change, so its derivative is 0.
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