9000065604
Level:
A
Find the area of the region bounded by the graph of
\(f(x)=\cos x\) on
\(\left [ \frac{\pi }{2};\pi \right ] \) and
lines \(y = 0\)
and \(x =\pi \).
\(1\)
\(\frac{3}
{4}\)
\(\frac{\sqrt{3}}
{2} \)
\(2\)
A
9000065509
Level:
A
Given the function
\[
F(x) = x + \frac{9}
{2}x^{2} + 9x^{3} + \frac{27}
{4} x^{4},
\]
find the function \(f\)
such that \(F\) is
primitive to \(f\)
on \(\mathbb{R}\).
\(f(x) = (1 + 3x)^{3}\)
\(f(x) = (1 + 3x)^{2}\)
\(f(x) = 1 + 3x + 3x^{2} + 3x^{3}\)
\(f(x) = (1 + 3x)^{4}\)
9000065605
Level:
A
Find the area of the region bounded by the curves
\(y = -2x\) and
\(y = -x^{2} + 3\).
\(\frac{32}
{3} \)
\(\frac{29}
{3} \)
\(\frac{31}
{3} \)
\(\frac{35}
{3} \)
9000065510
Level:
A
Given the function
\[
F(x) = \frac{6}
{7}x^{3}\sqrt{x},
\]
find the function \(f\)
such that \(F\) is
primitive to \(f\)
on the interval \((0;+\infty)\).
\(f(x) = 3x^{2}\sqrt{x}\)
\(f(x) = 3x\sqrt{x}\)
\(f(x) = 3x^{3}\sqrt{x}\)
\(f(x) = 7x\sqrt{x}\)
9000065606
Level:
A
Find the area of the region bounded by the curves
\(y =\mathrm{e} ^{x}\),
\(y = -\mathrm{e}^{x} + 2\) and
\(x = -3\).
\(4 + \frac{2}
{\mathrm{e}^{3}} \)
\(4 + \frac{1}
{\mathrm{e}^{3}} \)
\(4 -\frac{2}
{\mathrm{e}^{3}} \)
\(4 -\frac{1}
{\mathrm{e}^{3}} \)
9000065603
Level:
A
Find the area of the region bounded by the curves
\(y = 0\),
\(y = x^{3}\),
\(x = 1\) and
\(x = 3\).
\(20\)
\(22\)
\(24\)
\(26\)
9000065607
Level:
A
Find the area of the region bounded by the curves
\(y = 3^{x}\),
\(y = 3^{-x}\) and
\(y = 3\).
\(6 -\frac{4}
{\ln 3}\)
\(3 -\frac{2}
{\ln 3}\)
\(3 + \frac{4}
{\ln 3}\)
\(6 -\frac{2}
{\ln 3}\)
9000065609
Level:
A
Find the area of the region bounded by the curves
\(y = -x + 3\),
\(y = x^{2} - 3x\).
\(\frac{32}
{3} \)
\(8\)
\(\frac{8}
{3}\)
\(\frac{16}
{3} \)
9000063606
Level:
A
Find the following limit.
\[
\lim _{n\to \infty }\frac{3n^{2} - 2n + 1}
{2n^{3} - 4}
\]
\(0\)
\(\frac{3}
{2}\)
\(\frac{1}
{2}\)
\(-\frac{1}
{4}\)
9000063609
Level:
A
Find the following limit.
\[
\lim _{n\to \infty }\left ( \frac{n}
{n - 1} + \frac{n + 2}
{n + 1}\right )
\]
\(2\)
\(- 1\)
\(0\)
\(1\)