Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If f is a continuous function and <img alt="\mathrm{\int_0^x f(t) d t \rightarrow \infty as |x| \rightarrow \infty, }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cint_0%5Ex%

If f is a continuous function and \mathrm{\int_0^x f(t) d t \rightarrow \infty as |x| \rightarrow \infty, } then the numbers of points in which the line \mathrm{ y=m x } intersects the curve \mathrm{y^2+\int_0^x f(t) d t=2 } is

Option: 1

0


Option: 2

1


Option: 3

atmost 1
 


Option: 4

atleast 2


Answers (1)

best_answer

The point of intersection of the two curves are given by the solution of the equation,
\mathrm{(m x)^2+\int_0^x f(t) d t-2=0 . }
Let \mathrm{G(x)=(m x)^2+\int_0^x f(t) d t-2=0, G(0)=-2<0, G(\infty)=\infty>0 }\mathrm{and\, \, G(-\infty)=\infty \therefore \quad } By intermediate value property \mathrm{G(x)=0 } for atleast one value between \mathrm{0\, and\, \, \infty } and atleast one value between \mathrm{-\infty \, and\, 0 . }

Posted by

Anam Khan

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 2025: BTech in AI gains popularity; IIT, NIT cut-offs for artificial intelligence
anam-khan

JEE Main 2025 Live: NTA JEE session 1 begins tomorrow; admit card link, exam pattern, passing marks
anam-khan

JEE Main 2025 exam centre changed at UAE's Sharjah due to “unavoidable circumstances”

Latest Question