Download App

CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY3 Marks
Question
Determine that value of the constant 'k' so that function $\text{f(x)}=\begin{cases}\frac{\text{kx}}{|\text{x}|},&\text{if }\text{ x}<0\\3,&\text{if }\text{ x}\geq0\end{cases}$ is continuous at x = 0.
✓

Answer

Given, $\text{f(x)}=\begin{cases}\frac{\text{kx}}{|\text{x}|},&\text{if }\text{ x}<0\\3,&\text{if }\text{ x}\geq0\end{cases}$
Since, the function is continuous at x = 0, therefore,
$\lim\limits_{{\text{x}}\rightarrow0^-}\text{f(x})=\lim\limits_{{\text{x}}\rightarrow0^+}\text{f(x})=\text{f}(0)$
$\Rightarrow\lim\limits_{{\text{x}}\rightarrow0}\frac{-\text{kx}}{\text{x}}=\lim\limits_{{\text{x}}\rightarrow0}3=3$
$\Rightarrow-\text{k}=3$
$\Rightarrow\text{k}=-3$

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

Explore more

More "3 Marks Question" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Show that the line through the points (4, 7, 8) and (2, 3, 4) is parallel to the line through the points (-1, -2, 1) and, (1, 2, 5).
→
Evaluate the following intregals:
$\int\frac{\text{x}}{\sqrt{\text{x}^2+\text{x}+1}}\text{dx}$
→
Find the slopes of the tangent and the normal to the following curves at the indicated points:
$\text{y}=\sqrt{\text{x}}\ \text{at}\ \text{x}=9$
→
Evaluate the integral: $\int(x+1) \sqrt{x^2+x+1} d x$
→
Using Cofactors of elements of second row, evaluate $\triangle=\begin{vmatrix}5&3&8\\2&0&1\\1&2&3\end{vmatrix}.$
→
Construct the composition table for $+_5$ on set $S = \{0, 1, 2, 3, 4\}.$
→
Evaluate the following integrals:
$\int\frac{\text{x}^2\text{dx}}{\text{x}^6-\text{a}^6}\text{dx}$
→
Differentiate the following functions with respect to x:
$\tan(\text{x}^\circ+45^\circ)$
→
The cartesian equations of a line are x = ay + b, z = cy + d. Find its direction ratios and reduce it to vector form.
→
Using elementary transformation, find the inverse of each of the matrices, $\begin{bmatrix}3 & 10 \\2 & 7 \end{bmatrix}$
→