Download App

Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability1 Mark
Question
If the function $f(x)=\left\{\begin{array}{cc}3 x-8, & \text { if } x \leq 5 \\ 2 k, & \text { if } x>5\end{array}\right.$ is continuous, then the value of $k$ is
✓

Answer

 Since $f(x) $ is continuous at $ x=5 \text {, }$
$\Rightarrow \lim _{x \rightarrow 5} f(x)=\lim _{x \rightarrow 5^{+}} f(x)=f(5)$
$\Rightarrow 3(5)-8=2 k $
$\Rightarrow 7=2 k $
$\Rightarrow k=\frac{7}{2}$

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 Continuity and Differentiability→Continuity and Differentiability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Choose the correct answer from the given four options.
Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5)
Let F = 4x + 6y be the objective function Find the
Maximum of F - Minimum of F =
→
Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj} A|=64$. Then $|A|$ is equal to:
→
If $A=\left[a_{i j}\right]$ be a $3 \times 3$ matrix, where $a_{i j}=i-3 j$, then which of the following is false?
→
If A and B are two independent events with $\text{P(A)}=\frac{3}{5}$ and $\text{P(B)}=\frac{4}{9},$ then $\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$ equals,
  1. $\frac{4}{15}$
  2. $\frac{8}{45}$
  3. $\frac{1}{3}$
  4. $\frac{2}{9}$
→
If A and B are two events associated to a random experiment such that $\text{P}(\text{A}\cap\text{B})=\frac{7}{10}$ and $\text{P(B)}=\frac{17}{20}$, then P(A|B) =
  1. $\frac{14}{17}$
  2. $\frac{17}{20}$
  3. $\frac{7}{8}$
  4. $\frac{1}{8}$
→
The value of p and q for which the function $f ( x )=\left\{\begin{array}{cl}\frac{\sin (p+1) x+\sin x}{x} & , x<0 \\ \frac{q}{x^2} & , x=0 \\ \frac{\sqrt{x+b x^2}-\sqrt{x}}{x^{\frac{3}{2}}} & , x>0\end{array}\right.$ is continuous for all $x \in R$, are
→
The distance of the point (-3, 4, 5) from the origin:
  1. 50
  2. $5\sqrt{2}$
  3. 6
  4. None of these
→
The probability distribution of a discrete random variable X is given below:
$\text{X}:$ $2$ $3$ $4$ $5$
$\text{P}(\text{X}):$ $\frac{5}{\text{k}}$ $\frac{7}{\text{k}}$ $\frac{9}{\text{k}}$ $\frac{11}{\text{k}}$
The value of k is:
  1. 8
  2. 16
  3. 32
  4. 48
→
Choose the correct answer from the given four options.The value of $\sin^{-1}\bigg[\cos\Big(\frac{33\pi}{5}\Big)\bigg]$ is:
  1. $\frac{3\pi}{5}$
  2. $\frac{-7\pi}{5}$
  3. $\frac{\pi}{10}$
  4. $\frac{-\pi}{10}$
→
Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector $3 \hat{i}+2 \hat{j}-2 \hat{k}$
→