Home
Class 12
MATHS
If f(x)=|x^nn !2cosxcos(npi)/2 4sinxsin(...

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`

Text Solution

Verified by Experts

The correct Answer is:
0
`(d^(n))/(dx^(n))[f(x)]=|{:((d^(n))/(dx^(n))(x^(n)),n!,2),((d^(n))/(dx^(n))(cos x),cos (npi)/(2),4),((d^(n))/(dx^(n))(sin x), sin (npi)/(2),8):}|`
`=|{:(n!,n!,2),(cos(x+(npi)/(2)),cos""(npi)/(2),4),(sin(x+(npi)/(2)),sin""(npi)/(2),8):}|`
`"or "(d^(n))/(dx^(n))[f(x)]_(x=0)=0`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.9|14 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Single)|137 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.7|6 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

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 =|{:(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^3-x^2+a x+b is divisible by x^2-x , then find the value of f(2)dot

f(x)=e^x-e^(-x)-2sinx-2/3x^3dot Then the least value of n for which (d^n)/(dx^n)f(x)(""|)_(x=0)i snon z e roi s (a) 5 (b) 6 (c) 7 (d) 8

If f(x)=(a^x)/(a^x+sqrt(a ,)),(a >0), then find the value of g(n)= sum_(r=1)^(2n-1)2f(r/(2n)) g(4)

Find the domain of f(x)=sin^(-1)((x^2)/2)dot

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then find the value of f(7)dot

If (1+x+x^2++x^p)^n=a_0+a_1x+a_2x^2++a_(n p)x^(n p), then find the value of a_1+2a_2+3a_3+ddot+n pa_(n p)dot

If ("lim")_(xveca)[f(x)+g(x)]=2a n d ("lim")_(xveca)[f(x)-g(x)]=1, then find the value of ("lim")_(xveca)f(x)g(x)dot

If ("lim")_(tvecx)(e^tf(x)-e^xf(t))/((t-x)(f(x))^2)=2a n df(0)=1/2, then find the value of f^(prime)(0)dot a) 4 (b) 2 (c) 0 (d) 1