1003021108
Level:
B
Evaluate the following limit.
\[ \lim_{x\to\frac{\pi}4}\frac{\cos x-\sin x}{1-\mathrm{cotg}\,x} \]
\( -\frac{\sqrt2}{2} \)
\( \frac{\sqrt2}{2} \)
\( 0 \)
\( -\sqrt2 \)
Limits and continuity
1003021107
Level:
B
Evaluate the following limit.
\[ \lim_{x\to\pi}\frac{\mathrm{tg}\,x}{\sin2x} \]
\( \frac12 \)
\( -\frac12 \)
\( 0 \)
\( -2 \)
1003021106
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\rightarrow-3}\frac{x^2+5x+6}{x^3+27} \]
\( -\frac1{27} \)
\( -\frac5{27} \)
\( -\frac19 \)
\( \frac1{27} \)
1003021105
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\rightarrow1}\frac{x^2+x-2}{1-x^3} \]
\( -1 \)
\( 1 \)
\( 0 \)
\( 3 \)
1003021104
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\rightarrow-2}\frac{3x^2+3x-6}{2x^2-2x-12} \]
\( \frac9{10} \)
\( -\frac32 \)
\( \frac32 \)
\( 0 \)
1003021103
Level:
A
Evaluate the following limit.
\[ \lim\limits_{x\rightarrow-1}\frac{x^2+x-2}{x^3-1} \]
\( 1 \)
\( 0 \)
\( 2 \)
\( -2 \)
1003021102
Level:
B
Evaluate the following limit.
\[ \lim_{x\to\frac{\pi}4}\frac{1+\sin2x}{1-\cos4x} \]
\( 1 \)
\( 0 \)
\( 2 \)
\( \frac12 \)
1003021101
Level:
B
Evaluate the following limit.
\[ \lim_{x\to -2}\frac{2-\sqrt{x+6}}{x-2} \]
\( 0 \)
\( \frac14 \)
\( -\frac14 \)
\( 1 \)
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.
1103024505
Level:
A
Given the graph of the function \( f \), find \( \lim\limits_{x\rightarrow1^+}f(x) \).
\( 2 \)
\( 0 \)
\( -1 \)
does not exist