Download App

LIMITS AND DERIVATIVES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLIMITS AND DERIVATIVES4 Marks
Question
Find $\lim\limits_{\text{x}\rightarrow0}\text{f}(\text{x})$ and $\lim\limits_{\text{x}\rightarrow1}\text{f}(\text{x})$, where $\text{f}(\text{x})=\begin{cases}2\text{x}+3,& x \leq 0\\3(\text{x}+1), & x > 0\end{cases}$
✓

Answer

The given function is $\text{f}(\text{x})=\begin{cases}2\text{x}+3,& x \leq 0\\3(\text{x}+1), & x > 0\end{cases}$ $\lim\limits_{\text{x}\rightarrow0^-}\text{f}(\text{x})=\lim\limits_{\text{x}\rightarrow0}[2\text{x}+3]=2(0)+3=3$ $\lim\limits_{\text{x}\rightarrow0^+}\text{f}(\text{x})=\lim\limits_{\text{x}\rightarrow0}[3(\text{x}+1)]=3(0+1)=3$ $\therefore\lim\limits_{\text{x}\rightarrow0^-}\text{f}(\text{x})=\lim\limits_{\text{x}\rightarrow0^+}\text{f}(\text{x})=\lim\limits_{\text{x}\rightarrow0}\text{f}(\text{x})=3$ $\lim\limits_{\text{x}\rightarrow1^-}\text{f}(\text{x})=\lim\limits_{\text{x}\rightarrow1^+}3(\text{x}+1)=3(1+1)=6$ $\lim\limits_{\text{x}\rightarrow1^+}\text{f}(\text{x})=\lim\limits_{\text{x}\rightarrow1^+}3(\text{x}+1)=3(1+1)=6$ $\therefore\lim\limits_{\text{x}\rightarrow1^-}\text{f}(\text{x})=\lim\limits_{\text{x}\rightarrow1^+}\text{f}(\text{x})=\lim\limits_{\text{x}\rightarrow1}\text{f}(\text{x})=6$

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 "(Each question 4 marks)" from LIMITS AND DERIVATIVES→LIMITS AND DERIVATIVES — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}\tan\text{x}}{1-\cos2\text{x}}$
→
If O is the origin and Q is a variable point on $y^2 = x$, find the locus of the mid-point of OQ.
→
If $\text{x}+\text{iy}=\frac{\text{a}+\text{ib}}{\text{a}-\text{ib}},$ Prove that $\text{x}^2+\text{y}^2=1$
→
Show that the perpendicular bisectors of the sides of a triangle are concurrent.
→
In a group of 50 persons, 14 drink tea but not coffee and 30 drink tea. Find:
How may drink tea and coffee both.
→
If $\sec(\text{x}+\alpha)+\sec(\text{x}-\alpha)=2\sec\text{x},$ prove that $\cos\text{x}-\pm\sqrt{2}\cos\frac{\alpha}{2}$
→
Differentiate the following from first principle:$(\text{x}+2)^3$
→
How many triangles can be obtained by joining 12 points, five of which are collinear?
→
Express the following complex numbers in the form $\text{r}(\cos\theta+\text{i}\sin\theta):$ $1+\text{i}\tan\alpha$
→
For any two complex numbers $z_1$ and $z_2$, prove that $\operatorname{Re}\left(z_1 z_2\right)=\operatorname{Rez} z_1 \operatorname{Rez} z_2-\operatorname{Im} z_1 \mid m z_2$.
→