The value of k so that the function f(x) = l k(2x - x^2 ), ; ; ; … - Vidyadip

MCQ

The value of $k$ so that the function $f(x) = \left\{ \begin{array}{l}k(2x - {x^2}),\;\;\;{\rm{when\,}}\,x < 0\\\,\,\,\,\,\,\,\,\,\cos x,\,\,\,\,\,\,{\rm{when\,}}\,x \ge {\rm{0}}\end{array} \right.$ is continuous at $x = 0$, is

A
$1$
B
$2$
C
$4$
✓
None of these

✓

Answer

Correct option: D.

None of these

d
(d) $f(0 - ) = \mathop {\lim }\limits_{x \to 0 - } \,k(2x - {x^2}) = 0$;

$f(0 + ) = \mathop {\lim }\limits_{x \to 0 + } \,\cos x = 1$

$\therefore \,\,\,f(0) = \cos x = 1$

Hence no value of $k$ can make $f(0 - ) = 1.$

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

More "M.C.Q (1 Marks)" from STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let $A$ be a $2 \times 2$ matrix with real entries such that $A ^{\prime}=\alpha A + I$, where $\alpha \in R -\{-1,1\}$. If det $\left(A^2-A\right)=4$, then the sum of all possible values of $\alpha$ is equal to

The distance of the point $Q(0,2,-2)$ form the line passing through the point $\mathrm{P}(5,-4,3)$ and perpendicular to the lines $\overrightarrow{\mathrm{r}}=(-3 \hat{\mathrm{i}}+2 \hat{\mathrm{k}})$ $\lambda(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}), \quad \lambda \in \mathbb{R} \quad$ and $\quad \overrightarrow{\mathrm{r}}=(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}})+$ $\mu(-\hat{i}+3 \hat{J}+2 \hat{K}), \mu \in \mathbb{R}$ is

If P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6 then $\text{P}(\text{A}\cup\text{B})=$

Degree of the differential equation $y = a \left( {1 - {e^{\frac{{ - x}}{a}}}} \right)$, a being the parameter is

If $A$ and $B$ are square matrices of the same order, then $(A + B)(A - B)$ is equal to:

$\int {\frac{{\left( {x - 3} \right){e^x}}}{{{{\left( {x - 1} \right)}^3}}}\,dx}$ is equal to

If $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=4,\big|\vec{\text{a}}.\vec{\text{b}}\big|=2,$ then $|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2=$

If $A$ and $B$ are square matrices of same order and $|B| \neq 0$ then $(B^{-1}\,AB)^5$ is equal to

Which of the following equation is a linear differential equation of order $3\ ?\ [$Note: The original question asks for linear equation, but it should be linear differential equation$]:$

The value of $ \cos { \left( \tan ^{ -1 }{ \tan { 4 } } \right) }$ is-