Question
Evaluate the following one sided limits: $\lim\limits_{\text{x}\rightarrow-8^+}\frac{2\text{x}}{\text{x}+8}.$

Answer

$\lim\limits_{\text{x}\rightarrow-8^+}\frac{2\text{x}}{\text{x}+8}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{2(-8+\text{h})}{(-8+\text{h)+8}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{-16+2\text{h}}{\text{h}}$ $=\lim\limits_{\text{h}\rightarrow0}\frac{-16}{\text{h}}+2$ $\Rightarrow\frac{-16}{0}+2=-\infty$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Differentiate the following function with respect to $(\text{x})$:$\frac{\text{a}\cos\text{x}+\text{b}\sin\text{x}+\text{c}}{\sin\text{x}}$
If X and Y are two sets such that X $\cup$Y has 50 elements, X has 28 elements, and Y has 32 elements, how many elements does X $\cap$ Y have?
A die is thrown twice Each time the number appearing on it is recorded Describe the following events: C = sum of the numbers is less than Also, find A ∪ B, A ∩ B, A ∪ C, A ∩ C Which pairs of events are mutually exclusive?
Fill in the blanks in the following table:
  P(A) P(B) $\text{P}({\text{A}}\cap{\text{B}})$ $\text{P}({\text{A}}\cup{\text{B}})$
(i) $\frac{1}{3}$ $\frac{1}{5}$ $\frac{1}{15}$ .......
(ii) 0.35 .... 0.25 0.6
(iii) 0.5 0.35 .... 0.7
In a single throw of a die describe the following events: E = Getting an even number greater than 4
Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x - 7y + 5 = 0 and 3x + y = 0
A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher number.
Find the coordinates of the centre and radius of each of the following circles: $\text{x}^2 + \text{y}^2 + 6\text{x} − 8\text{y} − 24 = 0$
Find the sum of the following geometric progrssions:1, 3, 9, 27, ... to 8 terms
If f(x) = $ \left\{ {\begin{array}{*{20}{c}} {|x| + 1} \\ 0 \\ {|x| - 1} \end{array}} \right.\begin{array}{*{20}{c}} {x < 0} \\ {x = 0} \\ {x > 0} \end{array}$ for what values of a does $\mathop {\lim }\limits_{x \to a}$ f(x) exists?