Question
Which of the following functions has a removable discontinuity?
$\begin{array}{rlr}
f(x)=\frac{x^3-8}{x^2-4}, & & \text { for } x >2 \\
=3, & \text { for } x=2 \\
=\frac{e^{3(x-2)^2}-1}{2(x-2)^2}, & \text { for } x<2
\end{array}
$

Answer

Get the step-by-step solution for this question inside the Vidyadip app.

Get the answer in the app

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

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100m long is supported by vertical wires attached to the cable, the longest wire being 30m and the shortest wire being 6m. Find the length of a supporting wire attached to the roadway 18m from the middle.
Find the eccentricity, coordinates of foci, length of the latus-rectum of the following ellipse:$9\text{x}^2+25\text{y}^2=225$
A fair die is thrown two times. Find the probability that A: the sum of the numbers on them is 5.

B: the sum of the numbers on them is at least 8.

C: the first throw gives a multiple of 2 and the second throw gives a multiple of 3.

D: product of numbers on them is 12.

Evaluate the following limit:
$\text{f(x)}=\frac{\text{ax}^2+\text{b}}{\text{x}^2+1},\lim\limits_{\text{x}\rightarrow0}\text{ f(x)}=1 $ and $\lim\limits_{\text{x}\rightarrow\infty}\text{f(x)}=1,$ then prove that $\text{f}(-2)=\text{f}(2)=1.$
Find the minors and cofactors of elements of the determinants : $\left|\begin{array}{ccc}1 & -1 & 2 \\ 3 & 0 & -2 \\ 1 & 0 & 3\end{array}\right|$
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{{\pi}}}\frac{\sqrt{2+\cos\text{x}-1}}{(\pi-\text{x})^2}$
Find the equation of the tangent to the ellipse $\frac{x^2}{5}+\frac{y}{4}=1$ passing through the point (2,-2).
In a potato race 20 potatoes are placed in a line at intervals of 4 meters with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?
In any $\triangle\text{ABC},\frac{\text{b + c}}{12}=\frac{\text{c + a}}{13}=\frac{\text{a + b}}{15},$ then prove that $\frac{\cos\text{A}}{2}=\frac{\cos\text{B}}{7}=\frac{\cos\text{C}}{11}.$
Given that $t_{n+1}=5 t_{n+4}, t_1=4$, prove by method of induction that $t_n=5^n-1$.