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f(x)=e^x-e^(-x)-2sinx-2/3x^3dot Then the...

`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

A

5

B

6

C

7

D

8

Text Solution

Verified by Experts

`f(x)=e^(x)-e^(-x)-2 sin x -(2)/(3)x^(3)`
`f^(I)(x)=e^(x)+e^(-x)-2 cos x -2x^(2)`
`f^(II)(x)=e^(x)-e^(-x)+2 sin x-4x`
`f^(III)(x)=e^(x)+e^(-x)+2 cos x -4`
`f^(IV)(x)=e^(x)-e^(-x)-2 sin x`
`f^(V)(x)=e^(x)+e^(-x)-2 cos x`
`f^(VI)(x)=e^(x)-e^(-x)+2 sin x`
`f^(VII)(x)=e^(x)+e^(-x)+2 cos x`
`"Clearly, "f^(VII)(0)" is nonzero."`
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CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...

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  2. If y^(1/m)=(x+sqrt(1+x^2)),t h e n(1+x^2)y2+x y1 is (where yr represen...

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  3. If (sinx)(cosy)=1/2,t h e n(d^2y)/(dx^2)a t(pi/4,pi/4) is -4 (b) -2 (c...

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  4. A function f satisfies the condition f(x)=f^(prime)(x)+f^(x)+f^(x) ,w ...

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  5. Let f(x) be a polynomial of degree 3 such that f(3)=1,f^(prime)(3)=-1,...

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  6. If y^2=a x^2+b x+c ,t h e ny^3(d^(2y))/(dx^2) is a constant a functio...

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  7. If y=sinx+e^x ,t h e n(d^(2x))/(dy^2)= (-sinx+e^x)^(-1) (sinx-e^x)/(...

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  8. If f^(x)=-f(x)a n dg(x)=f^(prime)(x)a n d F(x)=(f(x/2))^2+(g(x/2))^2 ...

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  9. Let y=1n(1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal...

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  10. x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)at t=pi/2 is (a)(pi+4)/2 (b) ...

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  11. "Let "y=t^(10)+1 and x=t^(8)+1." Then "(d^(2)y)/(dx^(2)) is

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  12. If x = log p and y=(1)/(p), then

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  13. If x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2) is (varphi^(prime)psi^...

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  14. If f(x)=x^4tan(x^3)-x1n(1+x^2), then the value of (d^4(f(x)))/(dx^4) ...

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  15. Let g(x) be the inverse of an invertible function f(x), which is diffe...

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  16. f(x)=e^x-e^(-x)-2sinx-2/3x^3dot Then the least value of n for which (d...

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  17. Let y=f(x) and x=(1)/(z)." If "(d^(2)y)/(dx^(2))=lamda(z^(3))(dy)/(dz)...

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  18. Let x = f(t) and y = g(t), where x and y are twice differentiable func...

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  19. If f(x) satisfies the relation f((5x-3y)/2)=(5f(x)-3f(y))/2AAx ,y in ...

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  20. A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+...

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