9000064107
Level:
B
Find the tangent to the graph of the function
\(f(x) = x^{2} + 4x - 2\) parallel to
the line \(2x + y + 1 = 0\).
\(2x + y + 11 = 0\)
\(2x - y - 1 = 0\)
\(2x + y - 1 = 0\)
\(2x - y - 11 = 0\)
B
9000064108
Level:
B
Find the normal line to the graph of the function
\(f(x) = 2x^{2} - 7x\) parallel to
the line \(y = -x\).
\(x + y + 4 = 0\)
\(- x + y + 4 = 0\)
\(x - y - 8 = 0\)
\(x + y - 8 = 0\)
9000064109
Level:
B
Find the tangent to the graph of the function
\(f(x) = 3x^{2} - 8x + 2\) perpendicular
to the line \(x + 4y + 5 = 0\).
\(4x - y - 10 = 0\)
\(-4x + y + 1 = 0\)
\(8x - 2y + 1 = 0\)
\(-8x + 2y - 10 = 0\)
9000063809
Level:
B
Given the sequence \(\left ( \frac{1}
{n(n+1)}\right )_{n=1}^{\infty }\),
find the recurrence relation for this sequence.
\(a_{n+1} = \frac{n}
{n+2}a_{n},\ a_{1} = \frac{1}
{2}\)
\(a_{n+1} = \frac{n}
{n+1}a_{n},\ a_{1} = \frac{1}
{2}\)
\(a_{n+1} = \frac{n+1}
{n} a_{n},\ a_{1} = \frac{1}
{2}\)
\(a_{n+1} = \frac{n+1}
{n+2}a_{n},\ a_{1} = \frac{1}
{2}\)
9000064105
Level:
B
Find the tangent to the graph of the function
\(f(x) = x\sin x\) at the
point \(\left [ \frac{\pi }{2}; \frac{\pi } {2}\right ]\).
\(y = x\)
\(y = x + 1\)
\(y = 0\)
\(y =\pi -x\)
9000063407
Level:
B
In the following list find the value of the parameter
\(x\) which
ensure that the following geometric series is divergent.
\[
\sum _{n=1}^{\infty }(x + 4)^{2n}
\]
\(x = -5\)
\(x = -\frac{9}
{2}\)
\(x = -4\)
\(x = -\frac{7}
{2}\)
9000064106
Level:
B
Let \(p\) be the tangent to
the graph of the function \(f(x) = x^{2} + 4x - 2\)
perpendicular to the line \(x + 6y + 2 = 0\).
Find the point \(A\) where
\(p\) touches the graph
of the function \(f\).
\(A = \left [1;3\right ]\)
\(A = \left [-5;3\right ]\)
\(A = \left [-3;-5\right ]\)
\(A = \left [0;-2\right ]\)
9000063408
Level:
B
In the following list find the value of the parameter
\(x\) which
ensure that the following geometric series is divergent.
\[
\sum _{n=1}^{\infty }(5 - 3x)^{n}
\]
\(x = \frac{1}
{2}\)
\(x = \frac{13}
{9} \)
\(x = \frac{11}
{6} \)
\(x = \frac{5}
{3}\)
9000063802
Level:
B
We are given the sequence \(\left (an + b\right )_{n=1}^{\infty }\).
This sequence satisfies \(a_{4} - a_{1} = 6\). Use
this information to find \(a\).
\(a = 2\)
\(a = -2\)
\(a = -1\)
\(a = 1\)
9000063301
Level:
B
Differentiate the following function.
\[
f(x)=\sin (2x^{2} + 1)
\]
\(f'(x) = 4x\cos (2x^{2} + 1),\ x\in \mathbb{R}\)
\(f'(x) = 4x\cos x,\ x\in \mathbb{R}\)
\(f'(x) =\cos (4x),\ x\in \mathbb{R}\)
\(f'(x) =\sin (4x + 1),\ x\in \mathbb{R}\)