Introduction to limits Quiz 1

Question 1

Evaluate $$\mathop {\lim }\limits_{x 	o  - 2} \dfrac{{\left( {{x^2} - 4} ight)}}{{\left( {x + 2} ight)}}$$

Accepted Answer

$$ - 4$$

Answer

$$4$$

Answer

$$2$$

Answer

limit does not exist

Question 2

Evaluate $$\mathop {\lim }\limits_{x 	o \infty } \left( {\dfrac{{{2^x} + 3}}{{{3^x}}}} ight)$$

Accepted Answer

$$0$$

Answer

$$\dfrac{2}{3}$$

Answer

$$3$$

Answer

$$2$$

Question 3

Evaluate $$\mathop {\lim }\limits_{x 	o \infty } \left( {\dfrac{1}{{2 - \sqrt {x - 7} }}} ight)$$, if it exists.

Accepted Answer

$$0$$

Answer

$$\dfrac{{\sqrt 7 }}{2}$$

Answer

$$7$$

Answer

does not exist

Question 4

A function is given as $$f\left( x ight) = \left\{ {\begin{array}{*{20}{c}}  {6 - x\;\;\;\;\;\;\;\;x < 1} \   {4{x^2} + 2\;\;\;\;\;x \geqslant 1} \end{array}} ight\}$$. Calculate $$\mathop {\lim }\limits_{x 	o 1} f\left( x ight)$$, if it exists.

Accepted Answer

limit does not exist

Answer

$$1$$

Answer

$$6$$

Answer

$$5$$

Question 5

For a given function $$f\left( x ight) = \left\{ {\begin{array}{*{20}{c}}  {\dfrac{x}{3} + k\;\;\;\;\;\;x < 2} \   {\dfrac{{{x^2}}}{2} + 1\;\;\;\;\;x \geqslant 2} \end{array}} ight\}$$, if $$\mathop {\lim }\limits_{x 	o 2} f\left( x ight)$$ exists, then the value of $$k$$ is

Accepted Answer

$$k = \dfrac{7}{3}$$

Answer

$$k = 2$$

Answer

$$k = 3$$

Answer

$$k = \dfrac{3}{2}$$