1103024505
Level:
A
Given the graph of the function \( f \), find \( \lim\limits_{x\rightarrow1^+}f(x) \).
\( 2 \)
\( 0 \)
\( -1 \)
does not exist
Limits and continuity
1103024504
Level:
A
Given the graph of the function \( f \), find \( \lim\limits_{x\rightarrow1^-}f(x) \).
\( -1 \)
\( 0 \)
\( 2 \)
does not exist
1103024503
Level:
A
Given the graph of the function \( f \), find \( \lim\limits_{x\rightarrow1}f(x) \).
does not exist
\( -1 \)
\( 0 \)
\( 2 \)
1103024502
Level:
A
Given the graph of the function \( f \), find \( \lim\limits_{x\rightarrow0}f(x) \).
\[f(x)=\sin\!\left(\frac1x\right)\]
does not exist
\( a \)
\( -a \)
\( 0 \)
1103024501
Level:
A
Given the graph of the function \( f \), find \( \lim\limits_{x\rightarrow0}f(x) \).
\[f(x)=x^2\cdot\cos\!\left(\frac1x\right)+a,\ a\in\mathbb{R}\]
\( a \)
does not exist
\( 0 \)
\( a^2 \)
9000141901
Level:
A
Given the function \(f\),
find \(\lim _{x\to 1}f(x)\).
\[
f(x)=\begin{cases}
x^3+1 & \text{if } x\neq 1,\\
3 & \text{if } x = 1
\end{cases}
\]
\(2\)
\(3\)
\(1\)
Does not exist
9000141902
Level:
A
Given the function \(f\),
find \(\lim _{x\to \infty }f(x)\).
\[
f(x)=\begin{cases}
x^3+1 & \text{if } x\neq 1,\\
3 & \text{if } x = 1
\end{cases}
\]
\(\infty \)
\(-\infty \)
\(4\)
Does not exist
9000141903
Level:
A
Given the function \(g\),
find \(\lim _{x\to 1^{-}}g(x)\).
\[
g(x)=\begin{cases}
-\frac12(x-1)^2+2 & \text{if } x < 1,\\
\frac2{x^2}+1 & \text{if } x \geq 1
\end{cases}
\]
\(2\)
\(3\)
\(1\)
Does not exist
9000141904
Level:
A
Given the function \(g\),
find \(\lim _{x\to 1^{+}}g(x)\).
\[
g(x)=\begin{cases}
-\frac12(x-1)^2+2 & \text{if } x < 1,\\
\frac2{x^2}+1 & \text{if } x \geq 1
\end{cases}
\]
\(3\)
\(2\)
\(1\)
Does not exist
9000141908
Level:
A
Given the function \(h\),
find \(\lim _{x\to 1^{+}}h(x)\).
\[
h(x)=\begin{cases}
-\frac1{x-1} & \text{if } x< 1,\\
-(x-1)^2+2 & \text{if } x\geq 1
\end{cases}
\]
\(2\)
\(1\)
\(0\)
\(\infty \)
Does not exist