1003108105
Level:
B
Evaluate the integral \( \int\limits_0^1\frac{x-1}{x+3}\,\mathrm{d}x \).
\( 1+\ln\left(\frac34\right)^4 \)
\( 1-4\ln12 \)
\( 4\ln0.75 \)
\( 4\ln12 \)
B
1003108104
Level:
B
Evaluate the integral \( \int\limits_{-2}^0 (x+2)^3\,\mathrm{d}x \).
\( 4 \)
\( 28 \)
\( -28 \)
\( 12 \)
1003108103
Level:
B
Evaluate the integral \( \int\limits_{-1}^1\frac{x^2+3x-10}{x-2}\,\mathrm{d}x \).
\( 10 \)
\( 6 \)
\( 8 \)
\( 12 \)
1003108102
Level:
B
Evaluate the integral \( \int\limits_{-1}^1 \left(x^2-x\right)(x+1)\,\mathrm{d}x \).
\( 0 \)
\( \frac12 \)
\( 2 \)
\( 1 \)
1003108101
Level:
B
Evaluate the integral \( \int\limits_1^4\frac{\sqrt x-x+x^2}x\,\mathrm{d}x \).
\( 6.5 \)
\( 5.5 \)
\( 9.5 \)
\( 14.5 \)
1003189103
Level:
B
Find the product of all the nonnegative roots of the given equation.
\[ x^4- 13 x^2+ 36=0 \]
\( 6 \)
\( 0 \)
\( 5 \)
\( 13 \)
1003189102
Level:
B
Find the product of all the negative real roots of the given equation.
\[ x^4-34x^2+225=0 \]
\( 15 \)
The equation has no negative real roots.
\( 225 \)
\( -34 \)
1003189101
Level:
B
Find the sum of all the positive real roots of the given equation.
\[ x^4-116x^2+1600=0 \]
\( 14 \)
\( 116 \)
\( 0 \)
\( 16 \)
1103171402
Level:
B
There are graphs of three linear functions in the picture. Choose the formula which corresponds to all three functions.
\( y=dx-2;\ d\in\mathbb{R}^- \)
\( y=dx-2;\ d\in\mathbb{R}^+ \)
\( y=2x+d;\ d\in\mathbb{R}^- \)
\( y=-2x+d;\ d\in\mathbb{R}^+ \)
1103171401
Level:
B
There are graphs of three linear functions in the picture. Choose the formula which corresponds to all three functions.
\( y=m;\ m\in\mathbb{R}^- \)
\( y=m;\ m\in\mathbb{R}^+ \)
\( y=mx;\ m\in\mathbb{R}\setminus\{0\} \)
\( y=x+m;\ m\in\mathbb{R}^- \)