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)

?Which of the following is false

 Find the area of the shaded region where

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

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.

Find the result of

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

( Use L’Hôpital’s rule )

The result of

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

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

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

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

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 .

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

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

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)

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

. 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 ]             $g\left(x\right)=\frac1{\cos x}$

The result of

$\int_1^2ln2xdx$

: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)

Determine when the slope of the curve 𝑥

$x^2+xy-y^2=1$ 

is defined ?

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

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

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

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

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

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

Find the interval on which the function

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

?is decreasing

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

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

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

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

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 ]

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

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

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

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

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

Find the eccentricity of the hyperbola

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

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

 ? which of the following is false

Use the function

Find the point of the local minimum of the function

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

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

?Which of the following is true

The result of

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

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

،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 ):

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

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

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

The result of

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

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

If

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

 find the value of   f'(1/2)

Find the result of

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

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?

Which of the following functions has no horizontal tangent line ?

. The result of

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