Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Define as the product of two real functions <img alt="f_1(1)=x, x \in IR" src="https://entrancecorner.oncodecogs.co

Define f(x) as the product of two real functions f_1(1)=x, x \in IR and f_z(x)=\left\{\begin{array}{c}\sin \frac{1}{x}, \text { if } x=0 \\ 0, \text { if } x=0\end{array}\right. as follows f(x)=\left\{\begin{array}{r} f_1(x) \cdot f_2(x), \text { If } x \neq 0 \\ 0, \text { if } x=0 \end{array}\right. 
Statement I: f(x) is continuous on IR.
Statement II : f_1(x) and f_2(x) are continuous on IR.

Option: 1

Statement I is false, statement II is true.


Option: 2

Statement I is true, statement II is true. Statement II is a correct explanation of statement I.


Option: 3

Statement I is true, statement II is true. Statement II is not a correct explanation of statement I. 


Option: 4

Statement I is true, statement II is false. 


Answers (1)

best_answer

f(x)= \begin{cases}\sin \frac{1}{x}, & x \neq 0 \\ 0 & , x=0\end{cases}
To, check continuity at x=0,
$$ \underset{x\rightarrow 0^{+}}{lim} f(x)=0=\underset{x\rightarrow 0^{-}}{lim} f(x)=f(0)
So, continuous.
Statement I is correct.
\begin{aligned} f_2(x) & = \begin{cases}\sin \frac{1}{x}, & x \neq 0 \\ 0 & , x=0\end{cases} \\ \lim _{x \rightarrow 0} f_2(x) & =\lim _{x \rightarrow 0} \sin \left(\frac{1}{x}\right) \end{aligned}
it does not exist. 

Posted by

Kuldeep Maurya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026: NIT Rourkela records higher closing ranks in CSE, ECE, AI; core engineering branches stable
anam-khan

JEE Main 2026: IIT Delhi’s CSE, EE most opted; last 2 year’s closing ranks for all categories
anam-khan

Must provide CBSE 11th registration numbers to JEE Mains aspirants, board tells schools

Latest Question