پرسیاری وزاری بیرکاری 2022-2023 خولی دووەم ، خوێندنی ئینگلیزی

Which of the following parabolas has the line 𝑦=4 as its directrix?

$y-5=\frac14\left(x+2\right)^2$
$y+3=\frac14\left(x-1\right)^2$
$x-s=\frac14\left(y+4\right)^2$
$x+3=\frac14\left(y-2\right)^2$

Find the value of

$\lim_{x\rightarrow0}\frac x{\sqrt{x+1}-1}$

1-
$\frac12$
0
2

Which of the following is the horizontal asymptote to the function

$f\left(x\right)=\frac{1-\left|x\right|}{x+2}$

y=1
$y=\frac12$
y=0
$y=-\frac12$

Find the slant asymptote of the graph of the function

$f\left(x\right)=\frac{x^2+x-2}{x+3}$

y=x
y=x+2
y=x+4
y=x-2

If

$f\left(x\right)=\frac{-2}{\left(x-1\right)^2}$ find the value of

$\lim_{x\rightarrow1-}f\left(x\right)$

$-\infty$
$+\infty$
1-
0

Use the graph of 𝑓 on the right, at which value of 𝑥 is

𝑓′′(𝑥) < 0 ?

$\left[-\infty,-1\right]$
$\left[-\infty,0\right]$
$\left[0,+\infty\right]$
$\left[-1,1\right]$

Use integration to find the volume of the solid obtained by revolving the triangle
with vertices: ( 0 , 2 ) ، (3 , 0 ) ، (0 , 0 ) around the x-axis

$\frac{4\pi}3$
$4\pi$
$12\pi$
$6\pi$

If

$g\left(x\right)=\sqrt{2x^2-x+3}$ and $f\left(x\right)=3-x$

find the value of

‎$\lim_{x\rightarrow1}g\left(f\left(x\right)\right)$

1
2
3
4

Find the value of

$\lim_{x\rightarrow+\infty}\frac{3x^3+5}{2x^2+1}$

$-\infty$
$+\infty$
0
$\frac32$

An engineer in a certain factory wants to design an open box having
a square base and a surface area of 675 𝑐𝑚2 , as shown in the figure.
Choose the value of the height to produce a box of maximum volume?

h=12.5cm
h=6.5cm
h=7.5cm
h=15cm

If the function

$f\left(x\right)=\frac{ax+3}{b-2x}$

has a horizontal asymptote : 𝑦 = −2 and a vertical asymptote

$x=\frac52$

find the result of

3f(a)+5f'(b)

$\frac{-69}5$
$\frac{69}5$
$\frac{-121}5$
$\frac{121}5$

Find the equation of the tangent line to the function

$f\left(x\right)=x^2e^x+1$

at x=0

y=1
y=x+1
y=2x+1
y=-2x+1

If

$y=e^{\sin x}$

find

$\frac{dy}{dx}$

$\frac{dy}{dx}=y\cos x$
$\frac{dy}{dx}=\cos xe^{\cos x}$
$\frac{dy}{dx}=\sin xe^{\cos x}$
$\frac{dy}{dx}=ye^{\cos x}$

?Which of the following function discontinuous at 𝑥 = 1 and the discontinuity is removable

$f\left(x\right)=\frac{x^2+3x-4}{x^2-2x-1}$
$f\left(x\right)=\left\{\begin{array}{l}-2X+2\rightarrow x<1\\x\rightarrow x\geq1\end{array}\right.$
$f\left(x\right)=\frac s{\left|x-1\right|}$
$f\left(x\right)=\frac{x^3-1}{x-1}$

Find the x-intercept of the graph of the function:

$f\left(x\right)=3+\frac2x$

$\left(\frac{-3}2,0\right)$
$\left(\frac{-2}3,0\right)$
$\left(\frac13,0\right)$
$\left(\frac{-1}3,0\right)$

A (5 m) long ladder is leaning against a wall .The base of the ladder
is pulled away from the wall at a rate of (3 m/s). How fast is the top
of the ladder moving down the wall when the base is (4 m) from the wall?

$-6m/s$
$-\frac32m/s$
$-4m/s$
$-\frac72m/s$

?Which of the following verifying the condition 𝑓(−𝑥) ≠ −𝑓(𝑥)

$f\left(x\right)=\frac{3-x}x$
$f\left(x\right)=x^2+\sin x$
$f\left(x\right)=\cos2x$
All of them

Use the given graph to find the value of

‎ $\lim_{x\rightarrow2}f\left(x\right)$

0
4
2
بوونی نییە

Find the point of inflection for the function

$f\left(x\right)=2-\left(x-1\right)^2$

$\left(2,1\right)$
$\left(-1,-2\right)$
$\left(1,2\right)$
None

On which interval the given graph
of the function 𝑓 is decreasing?

$\left[-2,2\right]$
$\left[-1,0\right]$
$\left[-1,+\infty\right]$
$\left[1,3\right]$

Find the value of 𝑏 when the equation passes through the points (0 , 4) and (2 , 0) and
perpendicular to the line 𝑥 − 𝑏𝑦 + 1 = 0

$\frac{-1}2$
$\frac12$
6-
2

Find the vertical asymptotes of the function

$f\left(x\right)=\frac1{\tan x}$

$x=n\pi$
$x=\pi\left(n+\frac12\right)$
$x=2\left(n+\pi\right)$
$x=\pi\left(n-\frac12\right),n\in I$

By using symmetry, asymptotes, intercepts, first and second
derivative test determine the function of the given graph

$f\left(x\right)=\frac{4x}{x^2+1}$
$f\left(x\right)=\frac{-4x}{x^2+1}$
$f\left(x\right)=\frac{-4x}{2x^2+1}$
$f\left(x\right)=\frac{4x}{2x^2+1}$

Find b so that the points (0 , −5)، (1 , 𝑏 ) and (2 , −1) are collinear

0
2
$\frac12$
3-

Find the equation of the hyperbola. Vertices is: (2 , ±3) and passes through the point (0 , 5)

$\frac{y^2}9-\frac{4\left(x-2\right)^2}9=1$
$\frac{y^2}9+\frac{4\left(x-2\right)^2}9=1$
$\frac{y^2}9-\frac{9\left(x-2\right)^2}9=1$
$\frac{y^2}9+\frac{9\left(x-2\right)^2}9=1$

. Depending on the intermediate value theorem (IVT), which function achieve this condition
?( the equation 𝑓(𝑥) = 0 ) has a root between −1 𝑎𝑛𝑑 1

$f\left(x\right)=\frac x{x^2+1}$
$f\left(x\right)=x^3-5$
$f\left(x\right)=\frac1x$
$f\left(x\right)=\sqrt{3-2x}$

If the function

$f\left(x\right)=\left\{\begin{array}{l}x+1\rightarrow x\leq2\\ax+7\rightarrow x>2\end{array}\right.$

have no points of discontinuity ,find the value of

$\int_{2a}^a\left(3x^2+a\right)dx$‏

9
6
18
52

Determine the Domain and Range of the function

$f\left(x\right)=\frac3{2x-6}$

If

$f\left(x\right)=\frac{\cos2x}{x^2}$

then find the value of f'(π)

$\frac2{\pi^2}$
0
$\frac2{\pi^3}$
$-\frac2{\pi^3}$

Find the mean value of the functions

$f\left(x\right)=\sqrt x$

on the interval [0 , 4 ]

$\frac{16}3$
$\frac43$
$\frac83$
$\frac12$

If

f(x)=h(x) g(x)

, Find f'(1)

given: g(1)=1 , g'(1)=1 , h(1)=-2 , h'(1)=3

1-
0
1
6

Find

$\sqrt3$
$\frac1{\sqrt3}$
$\frac12$
$\frac1{\sqrt2}$

If you knowing that

and f'(x)=2x-1‏ f(-1)=5 ،

find the value of

$\lim_{x\rightarrow2}\frac{f\left(x\right)}{15}$

$\frac2{15}$
$\frac1{15}$
$\frac13$
$\frac15$

Find the derivative of the function

$f\left(x\right)=x\sqrt x$

f'(x)=$\frac1{3\sqrt x}$
f'(x)=$2\sqrt x$
f'(x)=$\frac{3\sqrt x}2$
f'(x)=$\sqrt x+\frac1{2\sqrt x}$

Find the second derivative of the function

f(x)=sin²x

‌f”(x)=sin2x
‌f”(x)=cos²x-sin²x
‌f”(x)=2cos2x
‌f”(x)=2sin2x

Find the distance between the point (−2 , 1 ) and the line 𝑦 = 𝑥 − 5

4
$4\sqrt2$
$2\sqrt2$
$3\sqrt2$

Find the value of (𝑓𝑜𝑔)′(2)

given that 𝑔(2) = −5 , 𝑓′(−5) = −1 and 𝑔′(2) = 4

20-
5
4-
20

Find

$\int\frac1{\left(3x\right)^{-2}}dx$

$3x^3+c$
$\frac1{3x^3}+c$
$\frac{-1}{9x^3}+c$
$9x^3+c$

Find the value of

$\int_0^\pi\cos^2x\sin xdx$

$-\frac13$
$\frac13$
$\frac23$
$-\frac23$

Which of the following function satisfying the given conditions:

f(0)=4 , f'(0)=0

f'(x)>0 for x>0 and f'(x)<0 for x<0

$f\left(x\right)=x^2+4$
$f\left(x\right)=x^3+4$
$f\left(x\right)=4-x^3$
$f\left(x\right)=-x^2+4$

Find

$\int lnxdx$

f(x) = Inx +x+c
‌f(x) = Inx² + c
f (x) = xInx -x+C
f(x) = xInx+x+c

Find the points of intersection of the two graph of the functions 𝑦 + 𝑥 = 5 and 3𝑥 − 4𝑦 = 8

$\left(3,2\right)$
$\left(1,4\right)$
$\left(-2,7\right)$
$\left(4,1\right)$

Find the slope of the tangent line to the equation

‏ $x^3y+x=-1$

at the point (1, −2)

5
5-
6
6-

Find the area of the region bound by the graph of the function

$f\left(x\right)=\sin x$

the 𝑥 − 𝑎𝑥𝑖𝑠 and the two lines 𝑥 = 0 and 𝑥 = 𝜋

1
2
3
4

Use the given graph of 𝑦 = 𝑓(𝑥) on the right
to determine the graph of the function 𝑦 = 𝑓(𝑥 + 2) + 5

If

$f\left(x\right)=\frac{-2}x$

Which of the following equals to f‘(-2)

Find the eccentricity of the ellipse

$4x^2+3y^2=12$

$\frac14$
$\frac{\sqrt3}2$
$\frac12$
$\frac34$

?Which of the following is true

$\lim_{x\rightarrow0}\frac{\left|x-1\left|-\right|x+1\right|}x=-2$
$\lim_{x\rightarrow3.6}\left[x-1\right]=3$
$\lim_{x\rightarrow2}\frac{2x^2-8}{2-x}=8$
$\lim_{\triangle x\rightarrow0}\frac{\cos\left(\pi+\triangle x)\pm1\right)}{\triangle x}=1$

An object moves according to the position function

$S\left(t\right)=t^3-6t^2+9t$‏

Find its acceleration at 𝑡 = 1

0
4
6-
9-

Which of the following is the equation of the asymptote to the hyperbol

$x^2-\frac{y^2}9=1$

$y=\frac13x$
$y=1+3x$
$y=-3x$
$y=\frac19x$

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