If f(x) = l a x^2 - b, 0 x < 1 2, ; x = 1 + 1, 1 < x 2 . is conti… - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}a{x^2} - b,{\rm{ }}0 \le x < 1\\2,\;{\rm{ }}x = 1\\x + 1,{\rm{ 1}} < x \le 2\end{array} \right.$ is continuous at $x = 1$, then the most suitable value of $a, b$ are

A
$a = 2,\;b = 0$
B
$a = 1,\;b = - 1$
C
$a = 4,\;b = 2$
D
All the above

✓

Answer

$\mathop {\lim }\limits_{x \to 1 - } f(x) = a - b,\mathop {\lim }\limits_{x \to 1 + } f(x) = 2 $
$\Rightarrow a - b = 2$
All the given sets of $a, b$ make $f(x)$ continuous at $x=1$.

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 a parabola $P$ be such that its vertex and focus lie on the positive $x$ - axis at a distance $2$ and $4$ units from the origin, respectively. If tangents are drawn from $O\,(0,0)$ to the parabola $P$ which meet $\mathrm{P}$ at $\mathrm{S}$ and $\mathrm{R}$, then the area (in $sq.\, units$) of $\triangle \mathrm{SOR}$ is equal to:

A differential equation of first order and first degree is

Let $K$ be the coefficient of $x^4$ in the expansion of $( 1 + x + ax^2) ^{10}$ . What is the value of $'a'$ that minimizes $K$ ?

Let the function, $f:[-7,0] \rightarrow R$ be continuous on $[-7,0]$ and differentiable on $(-7,0)$ If $f(-7)=-3$ and $f(x) \leq 2,$ for all $x \in(-7,0),$ then for all such functions $f, f(-1)+f(0)$ lies in the interval

The equation of an ellipse whose eccentricity is $1/2$ and the vertices are $(4, 0)$ and $(10, 0)$ is

Give the correct order of initials $T$ or $F$ for following statements. Use $T$ if statement is true and $F$ if it is false.
Statement $-1$ : If $A$ is an invertible $3 × 3$ matrix and $B$ is a $3 × 4$ matrix, then $A^{-1}B$ is defined
Statement $-2$ : It is never true that $A + B, A - B$, and $AB$ are all defined.
Statement $-3$ : Every matrix none of whose entries are zero is invertible.
Statement $-4$ : Every invertible matrix is square and has no two rows the same.

Let $X$ be a set containing $10$ elements and $P(X)$ be its power set. If $A$ and $B$ are picked up at random from $P(X),$ with replacement, then the probability that $A$ and $B$ have equal number elements, is

Let $f: R \rightarrow R$ be a function defined by $f( x )=( x -3)^{ n _{1}}( x -5)^{ n _{2}}, n _{1}, n _{2} \in N$. The, which of the following is $\underline{\text { NOT}} \;true? $

If z is a complex number, then the number of common roots of the equation $z^{1985}+z^{100}+1=0$ and $z^3+2 z^2+2 z+1=0$, is equal to :

If ${\cos ^{ - 1}}\frac{3}{5} - {\sin ^{ - 1}}\frac{4}{5} = {\cos ^{ - 1}}x,$ then $ x=$