#### Please solve RD Sharma class 12 chapter Continuity exercise 8.2 question 3 subquestion (iii) maths textbook solution

x = 0

Hint:

$\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$

Given:

$f(x)= \begin{cases}\frac{\sin x}{x} & x<0 \\ 2 x+3 & x \geq 0\end{cases}$

Explanation:

At x = 0

\begin{aligned} &\text { L.H.L }=\lim _{x \rightarrow 0^{-}} f(x)=\lim _{h \rightarrow 0}(0-h)=\lim _{h \rightarrow 0} \frac{\sin (-h)}{-h} \\ &=\lim _{h \rightarrow 0} \frac{-\sinh }{-h}=1 \end{aligned}

\begin{aligned} &\text { R.H.L }=\lim _{x \rightarrow 0^{+}} f(x)=\lim _{h \rightarrow 0}(0+h)=\lim _{h \rightarrow 0} \frac{\sinh }{h}=1 \\ &\text { Also } f(0)=2 \times 0+3=3 \\ &\text { Thus L.H.L}=\text {R.H.L} \neq \mathrm{f}(0) \end{aligned}

f is discontinuous at x = 0
The text passage contains a mathematical problem from a calculus textbook, specifically dealing with the continuity of a piecewise function at a point. The solution involves evaluating the left-hand limit, right-hand limit, and the function value at that point.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
#### Please solve RD Sharma class 12 chapter Continuity exercise 8.2 question 3 subquestion (iii) maths textbook solution

x = 0

Hint:

$\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$

Given:

$f(x)= \begin{cases}\frac{\sin x}{x} & x<0 \\ 2 x+3 & x \geq 0\end{cases}$

Explanation:

At x = 0

\begin{aligned} &\text { L.H.L }=\lim _{x \rightarrow 0^{-}} f(x)=\lim _{h \rightarrow 0}(0-h)=\lim _{h \rightarrow 0} \frac{\sin (-h)}{-h} \\ &=\lim _{h \rightarrow 0} \frac{-\sinh }{-h}=1 \end{aligned}

\begin{aligned} &\text { R.H.L }=\lim _{x \rightarrow 0^{+}} f(x)=\lim _{h \rightarrow 0}(0+h)=\lim _{h \rightarrow 0} \frac{\sinh }{h}=1 \\ &\text { Also } f(0)=2 \times 0+3=3 \\ &\text { Thus L.H.L}=\text {R.H.L} \neq \mathrm{f}(0) \end{aligned}

f is discontinuous at x = 0
user
The text passage contains a mathematical problem from a calculus textbook, specifically dealing with the continuity of a piecewise function at a point. The solution involves evaluating the left-hand limit, right-hand limit, and the function value at that point.

TYPE: SINGLE_QUESTION_WITH_ANSWER