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
\( 0 \)
\( a^2 \)
Limits and continuity
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
\( a \)
\( -a \)
\( 0 \)
1103024503
Level:
A
Given the graph of the function \( f \), find \( \lim\limits_{x\rightarrow1}f(x) \).
does not exist
\( -1 \)
\( 0 \)
\( 2 \)
1103024504
Level:
A
Given the graph of the function \( f \), find \( \lim\limits_{x\rightarrow1^-}f(x) \).
\( -1 \)
\( 0 \)
\( 2 \)
does not exist
1103024505
Level:
A
Given the graph of the function \( f \), find \( \lim\limits_{x\rightarrow1^+}f(x) \).
\( 2 \)
\( 0 \)
\( -1 \)
does not exist
1103024506
Level:
A
Given the graph of the function \( f \), find \( \lim\limits_{x\rightarrow-1}f(x) \).
\( 2 \)
\( 1 \)
\( -1 \)
This limit does not exist.
1103080001
Level:
A
The graph of the function \( f \) is given in the figure. Choose the incorrect statement. Dashed lines represent asymptotes of the function $f$.
\( \lim\limits_{x\rightarrow \infty} f(x) = -\infty \)
\( \lim\limits_{x\rightarrow -2^-} f(x) = -\infty \)
\( \lim\limits_{x\rightarrow \infty} f(x) = -2 \)
\( \lim\limits_{x\rightarrow -2} f(x) \) does not exist
1103080002
Level:
A
The graph of the function \( f \) is given in the figure. Choose the incorrect statement.
\( \lim\limits_{x\rightarrow-1}f(x) \) does not exist
\( \lim\limits_{x\rightarrow\infty} f(x) = \infty \)
\( \lim\limits_{x\rightarrow0} f(x) = 0 \)
\( \lim\limits_{x\rightarrow-\infty} f(x) = 1 \)
1103080003
Level:
A
The graph of the function \( f \) is given in the figure. Choose the incorrect statement.
\( \lim\limits_{x\rightarrow \infty} f(x) = -x \)
\( \lim\limits_{x\rightarrow 0^+} f(x) = 0 \)
\( \lim\limits_{x\rightarrow 0^-} f(x) = \infty \)
\( \lim\limits_{x\rightarrow-\infty} f(x) = \infty \)
1103080004
Level:
A
The graph of the function \( f \) is given in the figure. Choose the incorrect statement.
\( \lim\limits_{x\rightarrow1^-} f(x) = -1 \)
\( \lim\limits_{x\rightarrow -1} f(x) \) does not exist
\( \lim\limits_{x\rightarrow1^+} f(x) = 0 \)
\( \lim\limits_{x\rightarrow-\infty} f(x) = 1 \)