Download App

Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits3 Marks
Question
If $\text{f(x)}=\begin{cases}2\text{x}+3, & \text{x} \le0\\3(\text{x}+1), &\text{x} > 0\end{cases}$Find $\lim\limits_{\text{x}\rightarrow0}\text{f(x)}$ and $\lim\limits_{\text{x}\rightarrow1}\text{f(x)}.$
✓

Answer

$\lim\limits_{\text{x}\rightarrow0^+}\text{f(x)}=\lim\limits_{\text{x}\rightarrow0^+}3\text{(x}+1)=3$
And,
$\lim\limits_{\text{x}\rightarrow0^-}\text{f(x)}=\lim\limits_{\text{x}\rightarrow0^-}2\text{(x)}+3=3$
$\therefore\ \lim\limits_{\text{x}\rightarrow0}\text{f(x)}=3$
$\lim\limits_{\text{x}\rightarrow1}\text{f(x)}=\lim\limits_{\text{x}\rightarrow1}3(\text{x}+1)=3+3=6$
$\therefore\ \lim\limits_{\text{x}\rightarrow1}\text{f(x)}=6$

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 "Solve the Following Question.(3 Marks)" from Limits→Limits — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the equation of the straight line passing through $(3, -2)$ and making an angle of $60^\circ $ with the positive direction of $y-$axis.
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{(\text{x}+2)^{\frac{5}{2}}-(\text{a}+2)^{\frac{5}{2}}}{\text{x}-\text{a}}$
→
Find the square root of the following complex numbers:2(1 – √3 i)
→
The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of at least 65 marks.
→
Find the sum of the following series:
5 + 55 + 555 + ... to n terms.
→
Test whether the function
$f(x) = 5x – 3x^2,$ for $x \geq 1$
$= 3 – x,$ for $x < 1$
is differentiable at $x = 1.$
→
A bag contains 5 red, 4 blue and an unknown number m of green balls. If the probability

of getting both the balls green, when two balls are selected at random is $\frac{1}{7}$, find $m$.

→
How many numbers of two digit are divisible by $3?$
→
The ratio of the sum of first three term is to that of first $6$ terms of a G.P. is $125 : 152$. Find the common ratio.
→
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that:
$(\text{A}\cap\text{B})'=\text{A'}\cup\text{B'}$
→