Download App

CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY3 Marks
Question
Find which of the function:
$\text{f(x)}=\begin{cases}3\text{x}+5,&\text{if x}\geq2\\\text{x}^2,&\text{if x}<2\end{cases}$
at x = 2
✓

Answer

We have, $\text{f(x)}=\begin{cases}3\text{x}+5,&\text{if x}\geq2\\\text{x}^2,&\text{if x}<2\end{cases}$
At x = 2, $\text{L.H.L}​=​\lim\limits_{\text{x}\rightarrow2^-}(\text{x})^2$
$=\lim\limits_{\text{h}\rightarrow0}(2-\text{h}^2)=\lim\limits_{\text{h}\rightarrow0}(4+\text{h}^2-4\text{h})=4$
And $\text{R.H.L}=\lim\limits_{\text{x}\rightarrow2^+}(3\text{x}+5)$
$=\lim\limits_{\text{h}\rightarrow0}\big[3(2+\text{h})+5\big]=11$
Since, L.H.L ≠ R.H.L at x = 2
So, f(x) is discontinuous at x = 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 "3 Marks Question" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Differentiate the following functions with respect to x:
$\cos(\log\text{ x})^2$
→
ABCD is a parallelogram. If the coordinates of A, B, C are (-2, -1), (3, 0) and (1, -2) respectively, find the coordinates of D.
→
Let $\text{A}=\begin{bmatrix}2&-3\\-7&5\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\2&-4\end{bmatrix},$ verify that
$(\text{A}-\text{B})^\text{T}=\text{A}^\text{T}-\text{B}^\text{T}$
→
If A = {1, 2, 3}, show that a onto function f : A → A must be one-one.
→
Let A = {1, 2, 3,....., 9} and R be the relation in A x A defined by (a, b) R (c, d) if a + d = b + c for (a, b), (c, d) in A x A. Prove that R is an equivalence relation. Also obtain the equivalence class [(2,5)]
→
A random variable $X$ can take all non negative integral values and the probability that $X$ takes the value is proportional to $5^{-r}$. Find $P(X<3)$
→
Show that f : R → R, given by f(x) = x - [x], is neither one-one nor onto.
→
Solve the equation
$\cos^{-1}\frac{\text{a}}{\text{x}}-\cos^{-1}\frac{\text{b}}{\text{x}}=\cos^{-1}\frac{1}{\text{b}}-\cos^{-1}\frac{1}{\text{b}}-\cos^{-1}\frac{1}{\text{a}}$
→
Show that the relation R on the set A = {x ∈ Z; 0 ≤ x ≤ 12}, given by R = {(a, b): a = b}, is an equivalence relation. Find the set of all elements related to 1.
→
Differentiate the following functions with respect to x:
$\log(\tan^{-1}\text{x})$
→