Home
Class 12
MATHS
Let "f(x)"=|{:(pi^n,sinpix,cospix),((-1)...

Let `"f(x)"=|{:(pi^n,sinpix,cospix),((-1)^(n)!,-sin((npi)/2),-cos((npi)/2)),(-1,1/sqrt2,sqrt3/2):}|`
Then value or `d^n/(dx^n)["f(x)"]"at "x=1" is "`

A

0

B

1

C

-1

D

`1/sqrt2`

Text Solution

AI Generated Solution

To solve the problem, we need to evaluate the determinant given by the function \( f(x) \) and then find the \( n \)-th derivative of \( f(x) \) at \( x = 1 \). The function is defined as: \[ f(x) = \begin{vmatrix} \pi^n & \sin(\pi x) & \cos(\pi x) \\ (-1)^n n! & -\sin\left(\frac{n\pi}{2}\right) & -\cos\left(\frac{n\pi}{2}\right) \\ ...
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|12 Videos

  • DETERMINANTS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION A|33 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise section - J|6 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos

Similar Questions

Explore conceptually related problems

If f(x)=|{:(x^(n),sinx,cosx),(n!,"sin"(npi)/(2),"cos"(npi)/(2)),(a,a^(2),a^(3)):}| , then the value of (d^(n))/(dx^(n))(f(x))" at "x=0" for "n=2m+1 is

If f(x)=|(x^n, sinx, cosx),(n!, sin((npi)/2), cos((npi)/2)),(a, a^2,a^3)| , then show that d^n/dx^n [f(x)] at x=0 is 0

if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2),,8):}|, then find the value of (d^(n))/(dx^(n)) [f(x)]_(x=0) .(n in z).

If f(x)=|[x^n, n!, 2; cosx, cos((npi)/2), 4; sinx ,sin((npi)/2), 8]| then find the value of (d^n)/(dx^n)([f(x)])_(x=0)dot(n in z)dot

If f(x)=|x^nn !2cosxcos(npi)/2 4sinxsin(npi)/2 8| then find the value of (d^n)/(dx^n)([f(x)])_(x=0)dot(n in z)dot

For each ositive integer n, define a function f _(n) on [0,1] as follows: f _(n((x)={{:(0, if , x =0),(sin ""(pi)/(2n), if , 0 lt x le 1/n),( sin ""(2pi)/(2n) , if , 1/n lt x le 2/n), (sin ""(3pi)/(2pi), if, 2/n lt x le 3/n), (sin "'(npi)/(2pi) , if, (n-1)/(n) lt x le 1):} Then the value of lim _(x to oo)int _(0)^(1) f_(n) (x) dx is:

If y=cos^(-1){(2x-3sqrt(1-x^2))/(sqrt(13))},"f i n d"(dy)/(dx)

Let f(x)=int(x^2dx)/((1+x^2)(1+sqrt(x^2+1)))a n df(0)=0. Then value of f(1) will be

Let f(x)=(sin 2n x)/(1+cos^(2)nx), n in N has (pi)/(6) as its fundamental period , then n=

Let f(x)=lim_(nto oo) 1/n((x+1/n)^(2)+(x+2/n)^(2)+……….+(x+(n-1)/n)^(2)) Then the minimum value of f(x) is