Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The values of a and b such that the function f defined as <img alt="f(x)=\left\{\begin{array}{ll} a x^{2}-b, & |x|<1 \\ -1 /|x|, & |x| \geq 1 \end{array}\right. \text { is

The values of a and b such that the function f defined as

f(x)=\left\{\begin{array}{ll} a x^{2}-b, & |x|<1 \\ -1 /|x|, & |x| \geq 1 \end{array}\right. \text { is differentiable are }

Option: 1

\mathrm{a=1, b=-1}


Option: 2

\mathrm{a=1 / 2, b=1 / 2}


Option: 3

\mathrm{a=1 / 2, b=3 / 2}


Option: 4

none of these


Answers (1)

best_answer

Since every differentiable function is continuous, so we must have

\mathrm{\lim _{x \rightarrow 1^{-}} f(x)=f(1) \Rightarrow a-b=-1 }.

For f to be differentiable, \mathrm{f^{\prime}(1-)=f^{\prime}(1+)}

\mathrm{\Rightarrow \lim _{h \rightarrow 0-}\left[\frac{a(1+h)^{2}-b+1}{h}\right]=\lim _{h \rightarrow 0+}\left[\frac{-1 /|1+h|+1}{h}\right]}
\mathrm{\Rightarrow \lim _{h \rightarrow 0-}\left[\frac{a\left(2 h+h^{2}\right)}{h}\right]=\lim _{h \rightarrow 0+} \frac{h}{h(1+h)} (as \left.a-b=-1\right)}

\mathrm{\Rightarrow 2 a=1. Hence\: a=1 / 2 \: and \: b=3 / 2}.

Posted by

Gautam harsolia

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

BTech Admission 2025 Live: JEE Main correction window closes at 11:50 pm; VITEEE, SRMJEE, AEEE dates out
anam-khan

JEE Main 2025 application form correction begins at jeemain.nta.nic.in; editable fields
anam-khan

JEE Main 2025 application form correction window opens today; apply at jeemain.nta.nic.in

Latest Question