Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If <img alt="f(x)=\left|\begin{array}{lll} x^n & \sin x & \cos x \\ n ! & \sin (n \pi / 2) & \cos (n \pi / 2) \\ a & a^2 & a^3 \end{array}\right|" src="https://entrance

If f(x)=\left|\begin{array}{lll} x^n & \sin x & \cos x \\ n ! & \sin (n \pi / 2) & \cos (n \pi / 2) \\ a & a^2 & a^3 \end{array}\right| , then the value of  \frac{d^n}{d x^n}(f(x)) \text { at } x=0 \text { for } n=2 m+1 is 

Option: 1

-1


Option: 2

0


Option: 3

1

 


Option: 4

independent of a 


Answers (1)

best_answer

\frac{d^n}{d x^n}[f(x)]=\left|\begin{array}{ccc} \frac{d^n}{d x^n} x^n & \frac{d^n}{d x^n} \sin x & -\frac{d^n}{d x^n} \cos x \\ n ! & \sin (n \pi / 2) & \cos (n \pi / 2) \\ a & a^2 & a^3 \end{array}\right|

                      =\left|\begin{array}{ccc} n ! & \sin \left(\frac{n \pi}{2}+x\right) & \cos \left(\frac{n \pi}{2}+x\right) \\ n ! & \sin n \pi / 2 & \cos n \pi / 2 \\ a & a^2 & a^3 \end{array}\right| 

\therefore    At                                       \\\mathrm{x=0}\\ \: \: \: =0                                  \left[R_1=R_2\right]

Posted by

Divya Prakash Singh

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 aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today
anam-khan

JoSAA round 2 cut-off 2025 out; BTech closing ranks for top engineering courses at IITs
anam-khan

Goa Engineering Admission 2025: 1,415 eligible for BE seats; merit list on June 27

Latest Question