پرسیاری وزاری بیرکاری 2020-2021 خولی یەکەم ، خوێندنی ئینگلیزی

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

Find the result of

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

( Use L’Hopital’s rule )

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

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

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

If

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

?then which of the following is equal to

$\frac{dy}{dx}$

The result of

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

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

Find the third derivative of the function

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

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

The result of

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

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

Redefine the function

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

to be continuous at 𝑥 = 1

The result of

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

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

Find the equation of a line passing through the points

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

The result of

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

On which interval is the function

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

? decreasing

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

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

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

Find the point of inflection for the function

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

Find the result of

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

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

On which interval is the function

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

? convex

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

Determine the graph of the function

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

by using point plotting

? Which of the following is true

Determine the equation of the horizontal asymptote of the function

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

IF

f(x)=3ax³+3

is a function and

f'(3)=-162

find the result of 𝑓(2)

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

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

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

? Which of the following graphs represents a function

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

? Which of the following is false

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

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

 If

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

find the result of f'(π)

Find the result of

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

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

Find the derivative of the function

f(x)=xe^x

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

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

.Find the slope of the tangent line to the graph

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

at the point

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

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

Find the domain of the function 𝑔 ∘ 𝑓 when

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

 $g\left(x\right)=-\sqrt x$

The result of

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

Find the result of

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

If

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

then which of the following is equal to

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

Find the value of 𝒌 such that the line

$y=\frac34x+3$

is tangent to the graph of the function

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

The function

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

is always …………. in its domain