پرسیاری وزاری بیرکاری 2022-2023 خولی یەکەم ، خوێندنی ئینگلیزی

If 𝑓(𝑥) = −|2𝑥 + 3| + 6 and 𝑔(𝑥) = 6 − 𝑥 then find the value of 𝑥 where 𝑓(𝑥) = 𝑔(𝑥)

x=-3

Correct Incorrect Correct answer

x=-1

Correct Incorrect Correct answer

$\left\{\begin{array}{l}x=-3\\x=-1\end{array}\right.$

Correct Incorrect Correct answer

Has no value

Correct Incorrect Correct answer

?Which of the following is false

$\frac d{dx}\left(ln\frac3{x^4}\right)=\frac{-4}x$

Correct Incorrect Correct answer

$\frac d{dx}\left(3-2e^{4\pi}\right)=0$

Correct Incorrect Correct answer

$\frac d{dx}\left(\sin\sqrt x\right)=\frac{\cos x}{2\sqrt x}$

Correct Incorrect Correct answer

$\frac d{dx}=\left(\cos^2x\right)=-\sin2x$

Correct Incorrect Correct answer

Find the area of the shaded region where

‎$f\left(x\right)=\left(2-x\right)\sqrt x$

$\frac{12}{11}\sqrt2$

Correct Incorrect Correct answer

$\frac{11}{12}\sqrt2$

Correct Incorrect Correct answer

$\frac{15}{16}\sqrt2$

Correct Incorrect Correct answer

$\frac{16}{15}\sqrt2$

Correct Incorrect Correct answer

If the line passing through the points ( 3 , 𝑏 ) and ( −4 , 7 ) and that is perpendicular to the
line 2𝑥 − 3𝑦 + 8 = 0 then what is the value of 𝑏.

$\frac79$

Correct Incorrect Correct answer

$\frac{-7}2$

Correct Incorrect Correct answer

$\frac{35}3$

Correct Incorrect Correct answer

$\frac{-35}3$

Correct Incorrect Correct answer

Find the result of

$\lim_{x\rightarrow0}\frac{1-\cos4x}{1-\cos9x}$

( Use L’Hôpital’s rule )

$\frac38$

Correct Incorrect Correct answer

$\frac{16}{81}$

Correct Incorrect Correct answer

$\frac49$

Correct Incorrect Correct answer

$\frac12$

Correct Incorrect Correct answer

The result of

$\int_1^4\frac{x-2}{\sqrt x}dx$

$\frac43$

Correct Incorrect Correct answer

$\frac{-4}3$

Correct Incorrect Correct answer

$\frac23$

Correct Incorrect Correct answer

$\frac{-2}3$

Correct Incorrect Correct answer

The purchase price of a new machine is 22 850 000 dinars . Its value will decrease by 900 000
dinars each year . After how many years ( 𝑡 ) will the price of the machine become 15 650 000 dinars

t=5

Correct Incorrect Correct answer

t=8

Correct Incorrect Correct answer

t=9

Correct Incorrect Correct answer

t=12

Correct Incorrect Correct answer

$f\left(x\right)=5-2x^2$ وە $g\left(x\right)=3-X$ If

𝑥 then find the slope of the composite function (𝑓ᴏ𝑔)(𝑥)

0

Correct Incorrect Correct answer

3

Correct Incorrect Correct answer

8

Correct Incorrect Correct answer

5

Correct Incorrect Correct answer

A car was moving with a velocity of 60 m/s . The driver braked and the car stopped after 3 seconds Assuming that the acceleration of the car was constant during the pressure period Find the acceleration(a) and the distance (s)travelled by the car between the time the driver pressed the brakes and the stopping time .

$\left\{\begin{array}{l}a=-15m/s^2\\s=30m\end{array}\right.$

Correct Incorrect Correct answer

$\left\{\begin{array}{l}a=-18m/s^2\\s=60m\end{array}\right.$

Correct Incorrect Correct answer

$\left\{\begin{array}{l}a=-20m/s^2\\s=90m\end{array}\right.$

Correct Incorrect Correct answer

$\left\{\begin{array}{l}a=-30m/s^2\\s=135m\end{array}\right.$

Correct Incorrect Correct answer

$\lim_{x\rightarrow3}\frac{2x-6}{\sqrt{1+x}-2}$ The result of

8

Correct Incorrect Correct answer

2

Correct Incorrect Correct answer

$\frac12$

Correct Incorrect Correct answer

$\frac18$

Correct Incorrect Correct answer

? Which of the following functions is differentiable at 𝑥 = −2

Correct Incorrect Correct answer

𝑔 is the function defined by

$g\left(x\right)=\int_0^xf\left(t\right)dt$

where 𝑓 is the function whose graph is shown at the right . Evaluate 𝑔(6)

2

Correct Incorrect Correct answer

2-

Correct Incorrect Correct answer

8-

Correct Incorrect Correct answer

12

Correct Incorrect Correct answer

$\lim_{x\rightarrow4}\frac{\frac x{7-x}-\frac43}{x-4}$ :The result of

$\frac79$

Correct Incorrect Correct answer

$\frac{-7}2$

Correct Incorrect Correct answer

$\frac{-7}9$

Correct Incorrect Correct answer

$\frac{-9}7$

Correct Incorrect Correct answer

. Find the value of 𝑥 in the interval [ 0 , 𝜋 ] where the rates of change of the two functions

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

[are equal ] $g\left(x\right)=\frac1{\cos x}$

$x=\frac\pi4$

Correct Incorrect Correct answer

$x=\frac{3\pi}4$

Correct Incorrect Correct answer

$x=\frac\pi3$

Correct Incorrect Correct answer

$x=\frac{5\pi}3$

Correct Incorrect Correct answer

The result of

$\int_1^2ln2xdx$

6ln2-5

Correct Incorrect Correct answer

5ln2-3

Correct Incorrect Correct answer

4ln2-1

Correct Incorrect Correct answer

3ln2-1

Correct Incorrect Correct answer

:Which of the following graphs satisfies these conditions

$\lim_{x\rightarrow0}f\left(x\right)=2$ ; $\lim_{x\rightarrow2+}f\left(x\right)=3$ ; $\lim_{x\rightarrow-2}f\left(x\right)=0$ ; 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒d f(2)

Correct Incorrect Correct answer

Determine when the slope of the curve 𝑥

$x^2+xy-y^2=1$

is defined ?

$x\neq-2y$

Correct Incorrect Correct answer

$x\neq2y$

Correct Incorrect Correct answer

$x\neq4y$

Correct Incorrect Correct answer

$x\neq-4y$

Correct Incorrect Correct answer

Find the volume of the solid formed by revolving the region bounded by the graph of the functions

y=3-x² و y=2

around the x-axis

$\frac{32\pi}5$

Correct Incorrect Correct answer

$\frac{2\pi}3$

Correct Incorrect Correct answer

$\frac{32\pi}3$

Correct Incorrect Correct answer

$\frac{64\pi}3$

Correct Incorrect Correct answer

The vertical asymptotes of which of the following functions are 𝑥 = 1 + 2𝑛 . where 𝑛ϵI

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

None

Correct Incorrect Correct answer

Determine the equation of the horizontal asymptote to the graph of the
function

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

y=2

Correct Incorrect Correct answer

y=-2

Correct Incorrect Correct answer

y=1

Correct Incorrect Correct answer

y=-1

Correct Incorrect Correct answer

Find the equation of the parabola with focus 𝐹( 2 , 2 ) and directrix 𝑥 = −2

$\left(y+2\right)^2=8x$

Correct Incorrect Correct answer

$\left(y-2\right)^2=8x$

Correct Incorrect Correct answer

$\left(x+2\right)^2=8y$

Correct Incorrect Correct answer

$\left(x-2\right)^2=8y$

Correct Incorrect Correct answer

Use the given graph on the right, which of the following is true ?

The domain is R-{-1}

Correct Incorrect Correct answer

The y-intercept is ( 0 ، 1)

Correct Incorrect Correct answer

The range is R-{2}

Correct Incorrect Correct answer

3f(-1)-2f(0)=-2

Correct Incorrect Correct answer

Find the interval on which the function

$f\left(x\right)=x-4\sqrt{x+1}$ .

?is decreasing

$\rbrack-1,3\lbrack$

Correct Incorrect Correct answer

$\rbrack3,+\infty\lbrack$

Correct Incorrect Correct answer

$\rbrack-\infty,3\lbrack$

Correct Incorrect Correct answer

None

Correct Incorrect Correct answer

Which of the following is the equation of an asymptote of the graph of the hyperbola

$9\left(x+5\right)^2-4\left(y-3\right)^2=-36$

$y-3=\frac32\left(x+5\right)$

Correct Incorrect Correct answer

$y-3=\frac23\left(x+5\right)$

Correct Incorrect Correct answer

$y-3=\frac49\left(x+5\right)$

Correct Incorrect Correct answer

$y-3=\frac94\left(x+5\right)$

Correct Incorrect Correct answer

$f\left(x\right)=3-2\sqrt{x+1}$ Determine the graph of the function

Correct Incorrect Correct answer

Which of the following functions has a removable discontinuity at 𝑥 = 3
and non-removable discontinuity at 𝑥 = −3

$f\left(x\right)=\frac{2x+6}{x^2-9}$

Correct Incorrect Correct answer

$f\left(x\right)=\frac{x^2+3x}{x^2-9}$

Correct Incorrect Correct answer

$f\left(x\right)=\frac{x^2+8x+15}{x^2-9}$

Correct Incorrect Correct answer

$f\left(x\right)=\frac{x^2-x-6}{x^2-9}$

Correct Incorrect Correct answer

At which value of x does the function

$f\left(x\right)=\cos\left(\frac{\pi x}4\right)$

have an inflection point on the
interval [ 0 , 4 ]

$x=\frac12$

Correct Incorrect Correct answer

x=2

Correct Incorrect Correct answer

$x=\frac32$

Correct Incorrect Correct answer

x=3

Correct Incorrect Correct answer

Find the length of the major axis of the ellipse on the right

12

Correct Incorrect Correct answer

8

Correct Incorrect Correct answer

4

Correct Incorrect Correct answer

16

Correct Incorrect Correct answer

Which of the following functions is symmetric with respect to the y-axis ?

$f\left(x\right)=x^\frac12$

Correct Incorrect Correct answer

$f\left(x\right)=x^\frac13$

Correct Incorrect Correct answer

$f\left(x\right)=x^\frac32$

Correct Incorrect Correct answer

$f\left(x\right)=x^\frac23$

Correct Incorrect Correct answer

Depending on the indeterminate value theorem ( IVT ) , determine the function where the equation
𝑓(𝑥) = 0 has a root between -1 and 2

$f\left(x\right)=3x^3-6x+5$

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

$f\left(x\right)=-x^3+7x-2$

Correct Incorrect Correct answer

دووەم و سێهەم هەردووکیان

Correct Incorrect Correct answer

Use the intercepts , symmetry , asymptotes , first and second derivative test to determine the graph of the function ‏

$f\left(x\right)=\frac1x-x$

Correct Incorrect Correct answer

Find the eccentricity of the hyperbola

$4\left(y-1\right)^2-x^2=1$

$e=\frac52$

Correct Incorrect Correct answer

$e=\frac{\sqrt5}2$

Correct Incorrect Correct answer

$e=5$

Correct Incorrect Correct answer

$e=\sqrt5$

Correct Incorrect Correct answer

$\left[-\infty,4\right]$ The domain of which of the following functions is

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

Correct Incorrect Correct answer

$f\left(x\right)=-\sqrt{4-x}$

Correct Incorrect Correct answer

$f\left(x\right)=ln\left(4-x\right)$

Correct Incorrect Correct answer

$f\left(x\right)=-\left|4-x\right|$

Correct Incorrect Correct answer

? which of the following is false

Use the function

$\lim_{x\rightarrow2}f\left(x\right)=0$

Correct Incorrect Correct answer

$\lim_{x\rightarrow3-}f\left(x\right)=-3$

Correct Incorrect Correct answer

$\lim_{x\rightarrow0}f\left(x\right)=6$

Correct Incorrect Correct answer

$\lim_{x\rightarrow3}f\left(x\right)=0$

Correct Incorrect Correct answer

Find the point of the local minimum of the function

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

$\left(1,3\right)$

Correct Incorrect Correct answer

$\left(-1,3\right)$

Correct Incorrect Correct answer

$\left(0,0\right)$

Correct Incorrect Correct answer

None

Correct Incorrect Correct answer

$f\left(x\right)=\left\{\begin{array}{l}3-x\rightarrow x<3\\-\sqrt{x-3}\rightarrow x\geq3\end{array}\right.$ Determine the range of the function

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

$\left[-3,+\infty\right]$

Correct Incorrect Correct answer

R

Correct Incorrect Correct answer

?Which of the following is true

$\lim_{x\rightarrow\pi}\frac{\sin5x}{3x}=\frac53$

Correct Incorrect Correct answer

$\frac d{dx}\left(\frac{-3}{x^2+1}\right)=\frac6{\left(x^2+1\right)^2}$

Correct Incorrect Correct answer

$\int_0^3\left(x-2\right)\left(3x+1\right)dx=\frac{-3}2$

Correct Incorrect Correct answer

$\lim_{x\rightarrow+\infty}\frac{\left(3-2x\right)^2}{2x^2+1}=-2$

Correct Incorrect Correct answer

The result of

$\lim_{x\rightarrow+\infty}\frac{3x}{\cos2x}$

$\frac32$

Correct Incorrect Correct answer

0

Correct Incorrect Correct answer

$\frac23$

Correct Incorrect Correct answer

Does not exist

Correct Incorrect Correct answer

Find the equation of a horizontal line with 6 as an y-intercept

x=6

Correct Incorrect Correct answer

y=6

Correct Incorrect Correct answer

x=0

Correct Incorrect Correct answer

y=0

Correct Incorrect Correct answer

،If g and h are two differentiable function and $f\left(x\right)=\frac{g\left(x\right)}{h\left(x\right)} $ ,h(x)≠0

find the result of 𝑓´(1). knowing that

and the tangent line to the graph of a function h at the point ( 1 , 4 ) passes through the point ( 3 , 6 ):

$\frac7{16}$

Correct Incorrect Correct answer

$\frac9{16}$

Correct Incorrect Correct answer

$-\frac7{16}$

Correct Incorrect Correct answer

$-\frac9{16}$

Correct Incorrect Correct answer

An isosceles triangle is inscribed in a circle of diameter ( 12 cm ) . Find the maximum area of this
triangle

$12\sqrt3cm^2$

Correct Incorrect Correct answer

$24\sqrt3cm^2$

Correct Incorrect Correct answer

$27\sqrt3cm^2$

Correct Incorrect Correct answer

$36\sqrt3cm^2$

Correct Incorrect Correct answer

Use the given graph of the function 𝑦 = 𝑓(𝑥) on the right
to determine the graph of the function 𝑦 = −𝑓(𝑥 − 2) + 1

Correct Incorrect Correct answer

Which one is the equation of the tangent line to the graph of the function $f\left(x\right)=\sqrt{2-x}$ at x=-2

x + 4y = 6

Correct Incorrect Correct answer

3x – 2y =-10

Correct Incorrect Correct answer

4x – y= 6

Correct Incorrect Correct answer

x- 4y=-10

Correct Incorrect Correct answer

The result of

$\int\frac{x^3+1}{x^2}dx$

$\frac12x^2-\frac1x+c$

Correct Incorrect Correct answer

$\frac12x^2+\frac1x+c$

Correct Incorrect Correct answer

$\frac13x^2-\frac1x+c$

Correct Incorrect Correct answer

$x^2+\frac1x+c$

Correct Incorrect Correct answer

then find the value of 𝑏 . $f\left(x\right)=\frac{-3x^2-bx+5}{x+1}$ ، وە $f\left(-2\right)=-1$ If

b=1

Correct Incorrect Correct answer

b=2

Correct Incorrect Correct answer

b=3

Correct Incorrect Correct answer

b=4

Correct Incorrect Correct answer

If

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

find the value of f'(1/2)

$\frac32$

Correct Incorrect Correct answer

3

Correct Incorrect Correct answer

6

Correct Incorrect Correct answer

$-\frac32$

Correct Incorrect Correct answer

Find the result of

$\lim_{x\rightarrow0}\frac{\tan x\cos x}x$

1

Correct Incorrect Correct answer

0

Correct Incorrect Correct answer

3

Correct Incorrect Correct answer

Does not exist

Correct Incorrect Correct answer

A greenhouse can sell dwarf trees (6) years after they are planted. The function h′(𝑡) = 1.8𝑡 + 4 models
dwarf trees rate of growth in centimeter per year throughout the six years. The height of one dwarf tree
was ( 10.5 cm) when it was planted (t = 0). What will its height be when it is one year before sold?

69cm

Correct Incorrect Correct answer

56.5cm

Correct Incorrect Correct answer

53cm

Correct Incorrect Correct answer

75.5cm

Correct Incorrect Correct answer

Which of the following functions has no horizontal tangent line ?

$f\left(x\right)=\frac13x^3-3x^2+9x$

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

$f\left(x\right)=2x^3+x+1$

Correct Incorrect Correct answer

. The result of

is $\int\frac{\sin x}{\sqrt{\cos x}}dx$

$\frac12\sqrt{\cos x}+c$

Correct Incorrect Correct answer

$2\sqrt{\cos x}+c$

Correct Incorrect Correct answer

$\frac{-1}2\sqrt{\cos x}+c$

Correct Incorrect Correct answer

$-2\sqrt{\cos X}+C$

Correct Incorrect Correct answer

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