Your Progress 0 / 25 attempted
Q 01 / 25
If \(f(x)=3x+5\), then \(\lim\limits_{x\to 2} f(x)=11\).
Q 02 / 25
If \(\lim\limits_{x\to a} f(x)\) exists, then \(f(a)\) must be defined.
Q 03 / 25
\(\lim\limits_{x\to 0} \sin x = 0\).
Q 04 / 25
If \(\lim\limits_{x\to a^-} f(x)\neq \lim\limits_{x\to a^+} f(x)\), then \(\lim\limits_{x\to a} f(x)\) does not exist.
Q 05 / 25
\(\lim\limits_{x\to 1} \dfrac{x^2-1}{x-1}=2\).
Q 06 / 25
\(\lim\limits_{x\to 0} \dfrac{\sin x}{x}=1\).
Q 07 / 25
\(\lim\limits_{x\to 0} \dfrac{1}{x}\) exists.
Q 08 / 25
If \(f(x)=|x|\), then \(\lim\limits_{x\to 0} f(x)=0\).
Q 09 / 25
\(\lim\limits_{x\to 0} \dfrac{|x|}{x}=1\).
Q 10 / 25
If \(f'(a)\) exists, then \(f(x)\) is continuous at \(x=a\).
Q 11 / 25
If a function is continuous at \(x=a\), then it must be differentiable at \(x=a\).
Q 12 / 25
The derivative of a constant function is zero.
Q 13 / 25
If \(f(x)=x^2\), then \(f'(1)=2\).
Q 14 / 25
\(\lim\limits_{x\to 0} \dfrac{e^x-1}{x}=1\).
Q 15 / 25
If \(f'(a)=0\), then \(f(x)\) has a maximum or minimum at \(x=a\).
Q 16 / 25
\(\lim\limits_{x\to \infty} \dfrac{1}{x}=0\).
Q 17 / 25
If \(f(x)=x^3\), then \(f'(0)=0\).
Q 18 / 25
\(\lim\limits_{x\to 0} \dfrac{\tan x}{x}=1\).
Q 19 / 25
If \(\lim\limits_{x\to a} f(x)=\infty\), then the limit does not exist.
Q 20 / 25
\(\lim\limits_{x\to 0} x\sin\left(\dfrac{1}{x}\right)=0\).
Q 21 / 25
If \(f(x)=\sqrt{x}\), then \(f'(0)\) exists.
Q 22 / 25
If \(\lim\limits_{x\to a} f(x)\) and \(\lim\limits_{x\to a} g(x)\) exist, then \(\lim\limits_{x\to a}[f(x)+g(x)]\) exists.
Q 23 / 25
\(\lim\limits_{x\to 0} \dfrac{\sin x - x}{x}=0\).
Q 24 / 25
If \(f'(x)\) exists for all real \(x\), then \(f(x)\) is continuous for all real \(x\).
Q 25 / 25
\(\lim\limits_{x\to 0} \dfrac{e^x - \cos x - x}{x^2}=\dfrac{1}{2}\).
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