Find which of the function: f(x)= 3x+5,&if x 2 ^2,&if x<2 at x = … - Vidyadip

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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the mean and standard deviation of the following probability distributions:

$x_i $	$1$	$2$	$3$	$4$
$p_i $	$0.4$	$0.3$	$0.2$	$0.1$

Let $S$ be a relation on the set $R$ of all real numbers defined by $S = \{(a, b) \in R \times R: a^2 + b^2 = 1\}$ prove that $S$ is not an equivalence relation on $R.$

Differentiate the function $(\log x)^{\log x}, x > 1, \text{w.r.t}$ to $x.$

Show that the normals to the following parirs of planes are perpendicular other.
$\vec{\text{r}}\cdot(2\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}})=5$ and $\vec{\text{r}}\cdot(2\hat{\text{i}}-\hat{\text{j}}-2\hat{\text{k}})=5$

Determine whether the below relation is reflexive, symmetric and transitive:
Relation R in the set N of natural numbers is defined as
R = {(x, y) : y = x + 5 and x < 4}

Solve the following system of homogeneous linear equations:

2x + 3y + 4z = 0,

2x - y + 3z = 0

Let $A = R_0 \times R,$ where $R_0$ denote the set of all non$-$zero real numbers. A binary operation $'⊙\ '$ is defined on $A$ as follows: $(a, b) ⊙ (c, d) = (ac, bc + d)$ for all $(a, b), (c, d) \in R_0 \times R.$ Find the invertible elements in $A.$

For the principal values, evaluate the following:
$\sin^{-1}\Big(-\frac{\sqrt3}{2}\Big)-2\sec^{-1}\Big(2\tan\frac{\pi}{6}\Big)$

Find the second-order derivative of the function log(log x)

Evaluate the following integrals:
$\int\cos^5\text{x}\text{ dx}$