A function f is defined as follows, f(x) = * 20 c ,x & if , , ,x … - Vidyadip

MCQ

A function $f$ is defined as follows,

$f(x) =$ $\left\{ {\begin{array}{*{20}{c}} {\sin \,x}&{if\,\,\,x\,\, \leqslant \,\,c} \\ {ax\, + \,b}&{if\,\,\,x\,\, > \,\,c} \end{array}} \right.$ where $c$ is a known quantity.

If $f$ is derivable at $x = c$ , then the values of $'a'$ $and$ $'b’$ are _____ $and$______ respectively

A
$sin\, c \, and \,sin \,c - c \,cos\, c $
B
$sin\, c \, and \,sin \,c - c \,cos\, c $
C
$cos\, c \, and \,sin \,c+ c \,cos\, c $
✓
$cos\, c \, and \,sin \,c - c \,cos\, c $

✓

Answer

Correct option: D.

$cos\, c \, and \,sin \,c - c \,cos\, c $

d
. : $cos\, c \, \,and \,\,sin \,c - c \,cos\, c $

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $I(x)=\int \sqrt{\frac{x+7}{x}} d x$ and $I(9)=12+7 \log _e 7$ If I $(1)=\alpha+7 \log _e(1+2 \sqrt{2})$, then $\alpha^4$ is equal to $..........$.

If $A = \left[ {\begin{array}{*{20}{c}}{\,\,\,\cos \alpha }&{\sin \alpha }\\{ - \sin \alpha }&{\cos \alpha }\end{array}} \right]$, then ${A^2} = $

Let $\mathrm{g}: \mathrm{N} \rightarrow \mathrm{N}$ be defined as

$g(3 n+1)=3 n+2$

$g(3 n+2)=3 n+3$

$g(3 n+3)=3 n+1, \text { for all } n \geq 0$

Then which of the following statements is true?

The coefficient of ${x^5}$ in the expansion of ${({x^2} - x - 2)^5}$ is

For $z \in C$ if the minimum value of $(|z-3 \sqrt{2}|+|z-p \sqrt{2} i|)$ is $5 \sqrt{2}$, then a value of $P$ is $.......$

If $y = {x^x}$, then ${{dy} \over {dx}} = $

Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+7 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$. Let $L_{1}: \overrightarrow{\mathrm{r}}=(-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda \overrightarrow{\mathrm{a}}, \lambda \in \mathrm{R}$ and $L_{2}: \vec{r}=(\hat{j}+\hat{k})+\mu \vec{b}, \mu \in R$ be two lines. If the line $L_{3}$ passes through the point of intersection of $L_{1}$ and $L_{2}$, and is parallel to $\vec{a}+\vec{b}$, then $L_{3}$ passes through the point:

If $3{p^2} = 5p + 2$ and $3{q^2} = 5q + 2$, where $p \ne q$, then $pq$ is equal to

If $y=y(x)$ is the solution curve of the differential equation $\left(x^2-4\right) d y-\left(y^2-3 y\right) d x=0,$ $x>2, y(4)=\frac{3}{2}$ and the slope of the curve is never zero, then the value of $y(10)$ equals :

Let $O=(0,0)$ : let $A$ and $B$ be points respectively on $X$-axis and $Y$-axis such that $\angle O B A=60^{\circ}$. Let $D$ be a point in the first quadrant such that $A D$ is an equilateral triangle. Then, the slope of $D B$ is