Download App

Limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits3 Marks
Question
Find k so that $\lim\limits_{\text{x}\rightarrow2}\text{f(x)}$ may exist, where $\text{f(x)}=\begin{cases}2\text{x}+3, & \text{x}\le 2\\\text{x}+\text{k}, & \text{x} > 2\end{cases}.$
✓

Answer

$\lim\limits_{\text{x}\rightarrow2^-}\text{f(x)}=\lim\limits_{\text{x}\rightarrow2^-}(2\text{x}+3)$
$=2(2)+3$
$=7$
$\therefore\lim\limits_{\text{x}\rightarrow2^-}\text{f(x)}=7$
Also,
$\lim\limits_{\text{x}\rightarrow2^+}\text{f(x)}=\lim\limits_{\text{x}\rightarrow2^+}(\text{x}+\text{k})$
$=(2+\text{k})$
Since, $\lim\limits_{\text{x}\rightarrow2}\text{f(x)}$ exists (given)
$\therefore\ \lim\limits_{\text{x}\rightarrow2^-}\text{f(x)}=\lim\limits_{\text{x}\rightarrow2^+}\text{f(x)}$
$\Rightarrow7=2+\text{k}$
$\Rightarrow\text{k}=5$

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 "3 Marks Question" from Limits→Limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the middle terms(s) in the expansion of:
$\Big(3-\frac{\text{x}^{3}}{6}\Big)^{7}$
→
A carpenter was hired to build $192$ window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job$?$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\frac{\pi}{2}}}\frac{\sqrt{2}-\sqrt{1+\sin\text{x}}}{\cos^2\text{x}}$
→
Differentiate the following function with respect to x:$\text{e}^\text{x}\log\sqrt{\text{x}}\tan\text{x}$
→
A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.
→
Evaluate $\lim\limits_{\text{x}\rightarrow2}{\text{f(x)}}$ (if it exist), where $\text{f(x)}=\begin{cases}\text{x}-[\text{x}],&\text{x}<2\\4 ,& \text{x} = 2\\3\text{x}-5, & \text{x} > 2\end{cases}.$
→
Evaluate the following:
$(1+2\sqrt{\text{x}})^5+(1-2\sqrt{\text{x}})^5$
→
The first and the last terms of an A.P. area and I respectively. Show that the sum of $n^{th}$ term from the beginning and $n^{th}$ term from the end is $a + l.$
→
Find the ratio in which the sphere $x^2 + y^2 + z^2 = 504$ divides the line joining the points $(12, -4, 8)$ and $(21, -9, 18).$
→
A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:
  1. Exactly $3$ girls?
  2. At least $3$ girls?
  3. At most $3$ girls?
→