If f(x) is continuous on [-4,2], where f(x)= ll 6 b-3 a x, & for … - Vidyadip

MCQ

If $f(x)$ is continuous on $[-4,2]$, where $f(x)=\left\{\begin{array}{ll}6 b-3 a x, & \text { for }-4 \leq x<-2 \\ 4 x+1, & \text { for }-2 \leq x \leq 2\end{array}\right.$, then $a+b=$

A
$\frac{1}{6}$
B
$-\frac{1}{6}$
C
$\frac{7}{6}$
✓
$-\frac{7}{6}$

✓

Answer

Correct option: D.

$-\frac{7}{6}$

(D)
Since $f(x)$ is continuous on $[-4,2]$.
$\therefore \quad$ it is continuous at $x=-2$.
$\therefore \quad \lim _{x \rightarrow-2^{-}} f (x)=\lim _{x \rightarrow-2^{+}} f (x)$
$\Rightarrow \lim _{x \rightarrow-2^{-}}(6 b-3 a x)=\lim _{x \rightarrow-2^{+}}(4 x+1)$
$\Rightarrow 6 b-3 a (-2)=4(-2)+1$
$\Rightarrow 6 b+6 a=-7$
$\Rightarrow a + b =-\frac{7}{6}$

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 "MCQ" from Continuity→Continuity — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If the point $(2, k)$ lies outside the circles $x^2 + y^2 + x - 2y - 14 = 0$ and $x^2 + y^2 = 13$ then klies in the interval:

The equation of the smallest degree with real coefficients having $1 + i$ as one of the roots is:

If the line passing through (4, 3) and (2, k) is perpendicular to y = 2x + 3 then k =

Let $\text{f}(\text{x})=\text{x}-[\text{x}],\text{x}\in\text{R},$ then $\text{f}'\Big(\frac{1}{2}\Big)$ is :

If $f ( x )$ is continuous at $x=0$, where$f(x)=\left\{\begin{array}{ll}x^2+a, & x \geq 0 \\2 \sqrt{x^2+1}+b, & x<0\end{array}\right.$and $f\left(\frac{1}{2}\right)=2$, then the values of $a$ and $b$ are respectively

$\left(\frac{\sqrt{3}+ i }{2}\right)^6+\left(\frac{ i -\sqrt{3}}{2}\right)^6$ is equal to

The latus $-$ rectum of the conic $3\text{x}^2+4\text{y}^2-6\text{x}+8\text{y}-5=0$ is :

$\lim _{x \rightarrow 0} \frac{ e ^{1 / x}-1}{ e ^{1 / x}+1}=$

It is required to seat 5 men and 4 women in a row so that the men occupy odd places. Then the number of arrangements that are possible is

A function $f (x)$ is defined by $f (x)=\frac{ e ^x+ e ^{-x}-2}{x \sin x}$ for $x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}$. The value of $f(0)$ so that $f$ will be continuous in $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is