1003021103
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\rightarrow-1}\frac{x^2+x-2}{x^3-1} \]
\( 1 \)
\( 0 \)
\( 2 \)
\( -2 \)
Limits and continuity
1003021104
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\rightarrow-2}\frac{3x^2+3x-6}{2x^2-2x-12} \]
\( \frac9{10} \)
\( -\frac32 \)
\( \frac32 \)
\( 0 \)
1003021105
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\rightarrow1}\frac{x^2+x-2}{1-x^3} \]
\( -1 \)
\( 1 \)
\( 0 \)
\( 3 \)
1003021106
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\rightarrow-3}\frac{x^2+5x+6}{x^3+27} \]
\( -\frac1{27} \)
\( -\frac5{27} \)
\( -\frac19 \)
\( \frac1{27} \)
1003093101
Level:
A
Which of the statements A, B, C, D, E given bellow are correct?
\[ \begin{aligned}
\text{A: }& \lim\limits_{x\to1^+}\frac{2x}{x-1}=\infty \\
\text{B: }& \lim\limits_{x\to-2^+}\frac{x+1}{x+2}=-\infty \\
\text{C: }& \lim\limits_{x\to3^-}\frac{x+1}{3-x}=-\infty \\
\text{D: }& \lim\limits_{x\to-1^+}\frac{x}{x^2-1}=\infty \\
\text{E: }& \lim\limits_{x\to2^-}\frac{x+3}{4-x^2} =\infty
\end{aligned} \]
The only correct statements are:
A, B, D, E
A, B, D
A, D, E
A, B, C, E
A, B, C
B, D, E
1003093103
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\to\infty}\left(-2x^3+5x^2-7\right) \]
\( -\infty \)
\( \infty \)
\( -7 \)
\( 0 \)
1003093104
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\to-\infty}\left(x^4-3x^2-x+5\right) \]
\( \infty \)
\( -\infty \)
\( 5 \)
\( 0 \)
1003093105
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\to\infty}\frac{3x^2-1}{2-x} \]
\( -\infty \)
\( \infty \)
\( 3 \)
\( 0 \)
1003093106
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\to-\infty}\frac{3x^2+x-5}{x^2-2x+1} \]
\( 3 \)
\( \infty \)
\( -\infty \)
\( 0 \)
1003093107
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\to-\infty}\frac{x^2-2x+5}{2x^3-x^2+4} \]
\( 0 \)
\( \infty \)
\( -\infty \)
\( \frac12 \)