Let f(x) = l x^3 + x^2 - 16x + 20 (x - 2) ^2 , if ;x 2 ; ; ; ; ; … - Vidyadip

MCQ

Let $f(x) = \left\{ \begin{array}{l}\frac{{{x^3} + {x^2} - 16x + 20}}{{{{(x - 2)}^2}}},{\rm{if }}\;x \ne 2\\\;\;\;\;\;\,\;\;\;\;\;\;\;k\;\;\;\;\;\;\;\;,\;{\rm{if }}\;x = 2\end{array} \right.$ If $f(x)$ be continuous for all $x$, then $ k =$

✓
$7$
B
$-7$
C
$ \pm 7$
D
None of these

✓

Answer

Correct option: A.

$7$

a
(a) For continuous $\mathop {\lim }\limits_{x \to 2} \,f(x) = f(2) = k$

$ \Rightarrow \,\,k = \mathop {\lim }\limits_{x \to 2} \frac{{{x^3} + {x^2} - 16x + 20}}{{{{(x - 2)}^2}}}$

$ = \mathop {\lim }\limits_{x \to 2} \,\frac{{({x^2} - 4x + 4)\,\,(x + 5)}}{{{{(x - 2)}^2}}} = 7$

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

Choose the correct option from given four options:
$\int\tan^{-1}\sqrt{\text{x}}\text{ dx}$ is equal to:

If $A^3=O$, then $A^2+A+I=$

A line passes through the points $(6, -7, -1)$ and $(2, -3, 1)$. What are the direction ratios of the line?

Choose the correct answer from the given four options.If $\text{P}(\text{A})=0.4,\text{P}(\text{B})=0.8$ and $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)=0.6,$ then $\text{P}(\text{A}\cup\text{B})$ is equal to:

$\int_{0}^{\pi /2}{\frac{dx}{{{a}^{2}}{{\cos }^{2}}x+{{b}^{2}}{{\sin }^{2}}x}}\,=$

$r \times a = b \times a;\,\,r \times b = a \times b;\,\,a \ne 0;\,\,b \ne 0;\,\,a \ne \lambda b,\,\,$ $a $ is not perpendicular to $ b,$ then $r = $

Let $X_1$ and $X_2$ are optimal solutions of a $\ce{LPP},$ then:

The order and degree of the differential equation $\frac{{{d^2}y}}{{d{x^2}}} + {\left( {\frac{{dy}}{{dx}}} \right)^{\frac{1}{3}}} + {x^{\frac{1}{4}}} = 0$ are respectively

There are $6$ boxes labelled $B_1, B_2, \ldots, B_6$. In each trial, two fair dice $D_1, D_2$ are thrown. If $D_1$ shows $j$ and $D_2$ shows $k$, then $j$ balls are put into the box $B_k$. After $n$ trials, what is the probability that $B_1$ contains at most one ball ?

$\int {(1 + x - {x^{ - 1}}){e^{x + {x^{ - 1}}}}\,\,dx = } $