Home
Class 12
MATHS
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."`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Comprehension)|23 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|7 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)],a n d[3,f(3)] make angles pi/6,pi/3,a n dpi/4, respectively, with the positive direction of x-axis. Then the value of int_2^3f^(prime)(x)f^(x)dx+int_1^3f^(x)dx is equal to (a) -1/(sqrt(3)) (b) 1/(sqrt(3)) (c) 0 (d) none of these

For x in R , lim_(xrarroo)((x-3)/(x+2))^x is equal to (a) e (b) e^(-1) (c) e^(-5) (d) e^5

Instead of the usual definition of derivative Df(x), if we define a new kind of derivative D^*F(x) by the formula D*f(x)=lim_(h->0)(f^2(x+h)-f^2(x))/h ,w h e r ef^2(x) mean [f(x)]^2 and if f(x)=xlogx ,then D^*f(x)|_(x=e) has the value (A)e (B) 2e (c) 4e (d) none of these

Let f(x)=x^2a n dg(x)=sinxfora l lx in Rdot Then the set of all x satisfying (fogogof)(x)=(gogof)(x),w h e r e(fog)(x)=f(g(x)), is +-sqrt(npi),n in {0,1,2, dot} +-sqrt(npi),n in {1,2, dot} pi/2+2npi,n in { ,-2,-1,0,1,2} 2npi,n in { ,-2,-1,0,1,2, }

The domain of f(x)i s(0,1)dot Then the domain of (f(e^x)+f(1n|x|) is (a) (-1, e) (b) (1, e) (c) (-e ,-1) (d) (-e ,1)

Prove that (d^n)/(dx^n)(e^(2x)+e^(-2x))=2^n[e^(2x)+(-1)^n e^(-2x)]

If f(x) =(e^x)/(1+e^x), I_1=int(f(-a))^(f(a)) xg(x(1-x)dx, and I_2=int_(f(-a))^(f(a)) g(x(1-x))dx, then the value of (I_2)/(I_1) is (a) -1 (b) -2 (c) 2 (d) 1

If intsinx d(secx)=f(x)-g(x)+c ,t h e n f(x)=secx (b) f(x)=tanx g(x)=2x (d) g(x)=x

The n t h derivative of x e^x vanishes when (a) x=0 (b) x=-1 (c) x=-n (d) x=n

The domain of f(x)i s(0,1)dot Then the domain of (f(e^x)+f(1n|x|) is (-1, e) (b) (1, e) (-e ,-1) (d) (-e ,1)

CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. If graph of y=f(x) is symmetrical about the y-axis and that of y=g(x) ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. If y=asinx+bcosx ,t h e ny^2+((dy)/(dx))^2 is a function of x (b) func...

    Text Solution

    |

  9. (d)/(dx)sqrt((1-sin2x)/(1+sin2x)) is equal to, (0ltxltpi//4),

    Text Solution

    |

  10. If y = |cos x| + |sin x|,then (dy)/(dx)" at "x(2pi)/(3) is

    Text Solution

    |

  11. If f(x) =|log(e)|x||, then f'(x) equals

    Text Solution

    |

  12. If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to (a) -(cosx+sinx)...

    Text Solution

    |

  13. Instead of the usual definition of derivative Df(x), if we define a ne...

    Text Solution

    |

  14. If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/a ,t h e n(dy)/(dx) wherever it...

    Text Solution

    |

  15. The derivative of y=(1-x)(2-x)(n-x)a tx=1 is (b) (-1)(n-1)! n !-1 (d)...

    Text Solution

    |

  16. If y=sqrt((1-x)/(1+x)), prove that ((1-x^2)dy)/(dx)+y=0

    Text Solution

    |

  17. If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)),t h e n(dy)/(dx)i se...

    Text Solution

    |

  18. Let u(x) and v(x) be differentiable functions such that (u(x))/(v(x))=...

    Text Solution

    |

  19. If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to x/...

    Text Solution

    |

  20. Let h(x) be differentiable for all x and let f(x) = (kx=e^(x)) h(x) wh...

    Text Solution

    |