Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let  be a polynomial function such that <img alt="f(x)+f^{\prime}(x)+f^{\prime \prime}(x)=x^{5}+64" s

Let f(x) be a polynomial function such that f(x)+f^{\prime}(x)+f^{\prime \prime}(x)=x^{5}+64. Then the value of \lim _{x \rightarrow 1} \frac{f(x)}{x-1} is equal to:

Option: 1

-15


Option: 2

-60


Option: 3

60


Option: 4

15


Answers (1)

\mathrm{f(x)=(x-1)\left(x^{4}+a x^{3}+b x^{2}+c x+d\right)}
Hence,  \mathrm{f(x)+f^{\prime}(x)+f^{\prime \prime}(x)=x^{5}+(a+4) x^{4}+(b+3 a+16) x^{3}+(9 a+2 b+c-12) x^{2}+(d+c+4 b-6 a) x+(c-2 b)}

\mathrm{\because\: f(x)+f^{\prime}(x)+f^{\prime \prime}(x)=x^{5}+64}  \mathrm{\Rightarrow a+4=0, b+3 a+16=0,9 a+2 b+c-12=0 }
       , \mathrm{d+c+4 b-6 a=0 }
  \mathrm{\Rightarrow a=-4, b=-4, c=56, d=-64 }

\mathrm{So \: \: \lim _{x \rightarrow 1} \frac{f(x)}{(x-1)}=\lim _{x \rightarrow 1}\left(x^{4}-4 x^{3}-4 x^{2}+56 x-64\right) }
                                 \mathrm{=1-4-4+56-64 }
                                 \mathrm{=-15 }

Posted by

Kshitij

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 January 21 Shift 2 Analysis: Paper 'easy to moderate'; maths remains tough
anam-khan

Social media posts on JEE Main 2026 question paper leak fake, says NTA
anam-khan

JEE Main 2026: Digital ID proof invalid; latecomers won’t be allowed, NTA issues exam-day guidelines

Latest Question