پرسیاری وزاری بیرکاری 2020-2021 خولی یەکەم ، خوێندنی ئینگلیزی

? The line 𝑦 = −4𝑥 + 7 passes through which of the following points

(5,-3)

Correct Incorrect Correct answer

(-3,5)

Correct Incorrect Correct answer

(2,-1 )

Correct Incorrect Correct answer

(-1,2)

Correct Incorrect Correct answer

Find the result of

$\lim_{x\rightarrow+\infty}\frac{lnx^4}{x^3}$

( Use L’Hopital’s rule )

0

Correct Incorrect Correct answer

1

Correct Incorrect Correct answer

$\frac14$

Correct Incorrect Correct answer

$+\infty$

Correct Incorrect Correct answer

If 𝑓(𝑥) = 2𝑥 − 4 𝑎𝑛𝑑 𝑔(𝑥) = 1 + 3𝑥 , find the value of 𝑥 when 𝑓(𝑥) = 𝑔(𝑥)

x=-1

Correct Incorrect Correct answer

x=1

Correct Incorrect Correct answer

x=5

Correct Incorrect Correct answer

x=-5

Correct Incorrect Correct answer

Use the given graph on the right
to find the result of

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

0

Correct Incorrect Correct answer

1-

Correct Incorrect Correct answer

2

Correct Incorrect Correct answer

Does not exist

Correct Incorrect Correct answer

If

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

?then which of the following is equal to

$\frac{dy}{dx}$

$\frac{y+2x}{2y-x}$

Correct Incorrect Correct answer

$\frac{2x}{2y-x}$

Correct Incorrect Correct answer

$\frac{y-2x}{2y-x}$

Correct Incorrect Correct answer

$\frac{-2x}{2y-x}$

Correct Incorrect Correct answer

The result of

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

0

Correct Incorrect Correct answer

4-

Correct Incorrect Correct answer

4

Correct Incorrect Correct answer

$\frac45$

Correct Incorrect Correct answer

Depending on the intermediate value theorem (IVT). If the function f is continuous between
(𝑥 = 𝑎 and 𝑥 = 𝑏) , then the equation 𝑓(𝑥) = 0 has at least one root between two numbers a and b
when the signs 𝑓(𝑎) 𝑎𝑛𝑑 𝑓(𝑏) are

Positive

Correct Incorrect Correct answer

Negative

Correct Incorrect Correct answer

Opposite

Correct Incorrect Correct answer

None

Correct Incorrect Correct answer

Find the third derivative of the function

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

f”(x)=$\frac{-24}{x^4}$

Correct Incorrect Correct answer

f”(x)=$\frac{24}{x^4}$

Correct Incorrect Correct answer

f”(x)=$\frac{-96}{x^5}$

Correct Incorrect Correct answer

f”(x)=$\frac{96}{x^5}$

Correct Incorrect Correct answer

A farmer plans to fence a rectangular pasture adjacent to a river . The area of the pasture must
contain (51200 𝑚2) . What dimensions would be required for the least amount of fencing if
fencing is not needed along the river

256m , 200m

Correct Incorrect Correct answer

400m , 128m

Correct Incorrect Correct answer

512m , 100m

Correct Incorrect Correct answer

320m , 160m

Correct Incorrect Correct answer

The result of

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

0

Correct Incorrect Correct answer

1-

Correct Incorrect Correct answer

2-

Correct Incorrect Correct answer

Does not exist

Correct Incorrect Correct answer

The volume of a cube increases an average of (𝟑𝟔 𝑐𝑚3/𝑚𝑖𝑛)

while its surface area increases (𝟏𝟖 𝑐𝑚2/𝑚𝑖𝑛)

what is the length of the side of the cube

$2cm$

Correct Incorrect Correct answer

$4cm$

Correct Incorrect Correct answer

$2\sqrt2$

Correct Incorrect Correct answer

$8cm$

Correct Incorrect Correct answer

Redefine the function

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

to be continuous at 𝑥 = 1

$g\left(x\right)=\left\{\begin{array}{l}\frac{\sqrt{2-x}-\sqrt x}{x-1},x\neq1\\1,x=1\end{array}\right.$

Correct Incorrect Correct answer

$g\left(x\right)=\left\{\begin{array}{l}\frac{\sqrt{2-x}-\sqrt x}{x-1},x\neq1\\\sqrt2,x=1\end{array}\right.$

Correct Incorrect Correct answer

$g\left(x\right)=\left\{\begin{array}{l}\frac{\sqrt{2-x}-\sqrt x}{x-1},x\neq1\\0,x=1\end{array}\right.$

Correct Incorrect Correct answer

$g\left(x\right)=\left\{\begin{array}{l}\frac{\sqrt{2-x}-\sqrt x}{x-1},x\neq1\\-1,x=1\end{array}\right.$

Correct Incorrect Correct answer

The result of

$\lim_{x\rightarrow3-}\frac{2-x}{x-3}$

$-\infty$

Correct Incorrect Correct answer

$+\infty$

Correct Incorrect Correct answer

0

Correct Incorrect Correct answer

1-

Correct Incorrect Correct answer

In a fireworks festival, a rocket is launched upward .The function s(t)=-16t²+192t+4 is
the position function of the rocket, t is measured in seconds and S in feet
? What is the highest point the rocket can reach

404ft

Correct Incorrect Correct answer

580ft

Correct Incorrect Correct answer

606ft

Correct Incorrect Correct answer

768ft

Correct Incorrect Correct answer

Find the equation of a line passing through the points

$\left(-2,4\right)$ و $\left(-2,-4\right)$

x=-2

Correct Incorrect Correct answer

y=-2

Correct Incorrect Correct answer

y=-4

Correct Incorrect Correct answer

y=-2x-8

Correct Incorrect Correct answer

The result of

$\lim_{x\rightarrow-2}\frac{\frac1{x-1}-\frac13}{x+2}$

9

Correct Incorrect Correct answer

9-

Correct Incorrect Correct answer

$\frac{-1}9$

Correct Incorrect Correct answer

$\frac19$

Correct Incorrect Correct answer

On which interval is the function

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

? decreasing

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

Correct Incorrect Correct answer

$\left[-\infty,4\right]$

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

None

Correct Incorrect Correct answer

Assume that x and y are two differentiable of a variable t

y=x³+1 If

Find

$\frac{dx}{dy}$

at 𝑥 = 2 , by knowing that

$\frac{dy}{dx}=-3$

$\frac14$

Correct Incorrect Correct answer

$-\frac14$

Correct Incorrect Correct answer

$\frac12$

Correct Incorrect Correct answer

$\frac{-1}2$

Correct Incorrect Correct answer

? Which of the following functions has no vertical asymptote at 𝑥 = 2

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

$f\left(x\right)=\frac{\left|x+3\right|}{2x+6}$

Correct Incorrect Correct answer

Find the point of inflection for the function

$f\left(x\right)=3X\left(x-1\right)\left(x-2\right)$

(1,0)

Correct Incorrect Correct answer

(2,0)

Correct Incorrect Correct answer

(0,0)

Correct Incorrect Correct answer

None

Correct Incorrect Correct answer

Find the result of

$\lim_{x\rightarrow0}\frac{\sqrt{x+5}-\sqrt5}x$

$\frac1{\sqrt{10}}$

Correct Incorrect Correct answer

$2\sqrt5$

Correct Incorrect Correct answer

$\frac{-1}{\sqrt5}$

Correct Incorrect Correct answer

$\frac1{2\sqrt5}$

Correct Incorrect Correct answer

? Which of the following functions has a removable discontinuity at 𝑥 = −3

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

Correct Incorrect Correct answer

$f\left(x\right)=\frac{x^3+27}{2x+6}$

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

$f\left(x\right)=\frac{\left|x+3\right|}{2x+6}$

Correct Incorrect Correct answer

On which interval is the function

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

? convex

$\left[-1,1\right]$

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

𝑁𝑜𝑛e

Correct Incorrect Correct answer

If 𝑓 𝑎𝑛𝑑 𝑔 are two differentiable function for all x , and so are their derivatives.
? Which of the following is true

(f g' – f' g)'=f' g'' – f'' g'

Correct Incorrect Correct answer

f g'' + f'' g=(f g)''

Correct Incorrect Correct answer

(f' g')' = f'' g''

Correct Incorrect Correct answer

(f g)'' = f g'' + 2 f' g' + f'' g

Correct Incorrect Correct answer

Determine the graph of the function

|f(x)=2-|x+1

by using point plotting

Correct Incorrect Correct answer

? Which of the following is true

$\lim_{x\rightarrow+\infty}\left(2+\frac{\sin x}x\right)=2$

Correct Incorrect Correct answer

$\lim_{x\rightarrow2}\frac3{x-2}=3$

Correct Incorrect Correct answer

$\lim_{x\rightarrow1}\frac{x^2-1}{x-1}=0$

Correct Incorrect Correct answer

$\lim_{x\rightarrow0}\frac{\sin x}x=0$

Correct Incorrect Correct answer

Determine the equation of the horizontal asymptote of the function

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

$y=1$

Correct Incorrect Correct answer

$y=\frac{-3}2$

Correct Incorrect Correct answer

$y=\frac{-3}5$

Correct Incorrect Correct answer

$y=0$

Correct Incorrect Correct answer

IF

f(x)=3ax³+3

is a function and

f'(3)=-162

find the result of 𝑓(2)

2

Correct Incorrect Correct answer

51-

Correct Incorrect Correct answer

51

Correct Incorrect Correct answer

45-

Correct Incorrect Correct answer

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

$x^2y-x^2+3y=0$

Correct Incorrect Correct answer

$y=\sqrt{x-4}$

Correct Incorrect Correct answer

$y=\left|x+2\right|-2$

Correct Incorrect Correct answer

$x^2y-x=0$

Correct Incorrect Correct answer

For what value of 𝒂 , does the function

$f\left(x\right)=\left\{\begin{array}{l}ax^2+1,x\leq2\\2x-a,x>2\end{array}\right.$

?has no points of discontinuity

$\frac{-3}5$

Correct Incorrect Correct answer

$\frac{-5}3$

Correct Incorrect Correct answer

$\frac{-5}3$

Correct Incorrect Correct answer

$\frac35$

Correct Incorrect Correct answer

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

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

? Which of the following graphs represents a function

Correct Incorrect Correct answer

Find the equation of the line that passes through the point (−4 , 1 ) and perpendicular to
the 𝑦 – axis

x+4=0

Correct Incorrect Correct answer

y-4x=0

Correct Incorrect Correct answer

y-1=0

Correct Incorrect Correct answer

y+3=0

Correct Incorrect Correct answer

? Which of the following is false

The graph of a cubic function has exactly one point of inflection.

Correct Incorrect Correct answer

If f'(x)=g'(x) then f(x)=g(x)

Correct Incorrect Correct answer

If g(x)=-5f(x) then g'(x)=-5f'(x)

Correct Incorrect Correct answer

If $y=\frac{2x}\pi$ Then $\frac{dy}{dx}=\frac2\pi$

Correct Incorrect Correct answer

The given graph on the right shows the curve of the function 𝑓
On which interval is 𝑓′
increasing ?

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

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

Correct Incorrect Correct answer

Find the value of 𝒃 when the distance between the point( 1 , −3) and the line 3𝑥 − 𝒃𝑦 = 5 is (𝑧𝑒𝑟𝑜)

$\frac32$

Correct Incorrect Correct answer

$-\frac32$

Correct Incorrect Correct answer

$\frac23$

Correct Incorrect Correct answer

$-\frac23$

Correct Incorrect Correct answer

If

f(x) = 2(sin x) (cos x)

find the result of f'(π)

2π

Correct Incorrect Correct answer

2π-

Correct Incorrect Correct answer

2

Correct Incorrect Correct answer

2-

Correct Incorrect Correct answer

Find the result of

$\lim_{x\rightarrow0}\frac{\frac5{2x+10}-\frac12}x$

$\frac52$

Correct Incorrect Correct answer

$-\frac1{20}$

Correct Incorrect Correct answer

$-\frac1{10}$

Correct Incorrect Correct answer

0

Correct Incorrect Correct answer

. Determine the range of the function 𝑓
from the given graph on the right

$\left[2,-2\right]$

Correct Incorrect Correct answer

$\left[-2,1\right]$

Correct Incorrect Correct answer

$\left[-1,2\right]$

Correct Incorrect Correct answer

$\left[0,2\right]$

Correct Incorrect Correct answer

Find the derivative of the function

f(x)=xe^x

f ‘(x) = e^x

Correct Incorrect Correct answer

f ‘(x) = e^x(x+1)

Correct Incorrect Correct answer

f ‘(x) = e^x+1

Correct Incorrect Correct answer

f ‘(x) = xe^x+1

Correct Incorrect Correct answer

The figure on the right shows a rectangle and an isosceles triangle
inscribed in a circle of diameter (5) . What is the value of (x) that will
?make the areas of the rectangle and the triangle equal

3/5

Correct Incorrect Correct answer

2/5

Correct Incorrect Correct answer

1

Correct Incorrect Correct answer

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 )

Correct Incorrect Correct answer

.Find the slope of the tangent line to the graph

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

at the point

$\left(2,\sqrt3\right)$

$\frac1{\sqrt3}$

Correct Incorrect Correct answer

$-\frac1{\sqrt3}$

Correct Incorrect Correct answer

$-\frac2{\sqrt3}$

Correct Incorrect Correct answer

$\frac2{\sqrt3}$

Correct Incorrect Correct answer

Which of the following functions has a vertical asymptote at 𝑥 = 3 and
? slant asymptote at 𝑦 = −2𝑥

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

Correct Incorrect Correct answer

$f\left(x\right)=\frac{-2x^2+6x+1}{x-3}$

Correct Incorrect Correct answer

$f\left(x\right)=\frac{-4x^2-18x}{2x-6}$

Correct Incorrect Correct answer

$f\left(x\right)=\frac{-x^2+12x}{x-3}$

Correct Incorrect Correct answer

Find the domain of the function 𝑔 ∘ 𝑓 when

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

$g\left(x\right)=-\sqrt x$

$\left[-2,2\right]$

Correct Incorrect Correct answer

$\left[0,2\right]$

Correct Incorrect Correct answer

$\left[-\infty,-2\right]\cup\left[2,+\infty\right]$

Correct Incorrect Correct answer

$\left[-2,0\right]$

Correct Incorrect Correct answer

The result of

$\lim_{\Delta x\rightarrow0}\frac{-3{(x+\Delta x)}^2+3x^2}{\Delta x}$

6x

Correct Incorrect Correct answer

6x-

Correct Incorrect Correct answer

3x²

Correct Incorrect Correct answer

-3x²

Correct Incorrect Correct answer

Find the result of

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

3-

Correct Incorrect Correct answer

3

Correct Incorrect Correct answer

$+\infty$

Correct Incorrect Correct answer

0

Correct Incorrect Correct answer

If

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

then which of the following is equal to

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

$x^2-2x$

Correct Incorrect Correct answer

$x^2+2x$

Correct Incorrect Correct answer

$x^2+2x+4$

Correct Incorrect Correct answer

$x^2-2x+4$

Correct Incorrect Correct answer

Find the value of 𝒌 such that the line

$y=\frac34x+3$

is tangent to the graph of the function

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

k=2

Correct Incorrect Correct answer

k=-2

Correct Incorrect Correct answer

k=3

Correct Incorrect Correct answer

k=-3

Correct Incorrect Correct answer

The function

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

is always …………. in its domain

Increasing

Correct Incorrect Correct answer

Decreasing

Correct Incorrect Correct answer

Concave

Correct Incorrect Correct answer

Convex

Correct Incorrect Correct answer

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