Home
Class 12
MATHS
if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/...

`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).`

Text Solution

Verified by Experts

` (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)) (sinx),,sin .(npi)/(2),,8):}|`
`=|{:(n!,,n!,,2),(cos (x+(npi)/(2)),,cos .(npi)/(2),,4),(sin (x+(npi)/(2)),,sin .(npi)/(2),,8):}|( n in Z)`
`rArr (d^(n))/(dx^(n)) [f(x)]_(x=0) =0" "(:' C_(1) " and " C_(2) " are same)"`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

If x satisfies x^(2)-2x cos theta +1=0 , then the value of x^(n)+((1)/(x^n)) is

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

If 2tan^2x-5secx=1 for exactly seven distinct value of x in [0,(npi)/2],n in N then find the greatest value of ndot

Find the period of f(x)=sin((pix)/(n !))-cos((pix)/((n+1)!))

If 2 sin^(2) ((pi//2) cos^(2) x)=1-cos (pi sin 2x), x ne (2n + 1) pi//2, n in I , then cos 2x is equal to

Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value of n is________

If |[x^n, x^(n+2),x^(2n)],[1,x^a, a],[x^(n+5),x^(a+6),x^(2n+5)]|=0,AAx in R ,where n in N , then value of a is (a) n (b) n-1 (c) n+1 (d) none of these

If sinx+cos e cx=2, then sin^n x+cos e c^n x is equal to 2 (b) 2^n (c) 2^(n-1) (d) 2^(n-2)

If sin^(-1)x_1+sin^(-1)x_2++sin^(-1)x_nlt=-(npi)/2,n in N ,n=2m+1, mgeq1, then find the value of (x_1^1+x_3^3+x_5^5+...(m+1)t e r m s)/(x_2^2+x_4^ 4+x_6^ 6+.... mt e r m s)

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

CENGAGE-DETERMINANTS-All Questions
  1. If f,g,a n dh are differentiable functions of xa n d(x)=|fgh(xf)'(xg...

    Text Solution

    |

  2. If, a,b,c are positive and unequal,show that value of the determinant ...

    Text Solution

    |

  3. if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2)...

    Text Solution

    |

  4. Without expanding a determinant at any stage, show that ||x^2+x ,x+1 ,...

    Text Solution

    |

  5. Show that |{:(bc-a^(2),,ca-b^(2),,ab-c^(2)),(ca-b^(2),,ab-c^(2),,bc-a^...

    Text Solution

    |

  6. Show that the system of equations 3x-y + 4z = 3, x + 2y-3z =-2 and 6x ...

    Text Solution

    |

  7. Show that |{:( 2bc-a^2 , c^2 ,b^2),(c^2 , 2ca-b^2 , a^2),(b^2 , a^2 , ...

    Text Solution

    |

  8. If y=|sinxcosxsinxcosx-sinxcosxx1 1|=fin d(dy)/(dx)dot

    Text Solution

    |

  9. Consider the system of equation x+y+z=6,x+2y+3z=10 ,a n dx+2y+lambdaz=...

    Text Solution

    |

  10. Consider the system of linear equations in x , ya n dz : ""(sin3theta...

    Text Solution

    |

  11. Prove without expansion that |a h+bgga b+c h bf+b afh b+b c af+b cc bg...

    Text Solution

    |

  12. If alpha,beta "and" gamma are real number without expanding at any sta...

    Text Solution

    |

  13. If 3 digit numbers A28, 3B9 and 62C are divisible by a fixed constant ...

    Text Solution

    |

  14. If a=costheta+isintheta,b=cos2theta-isin2theta,c=cos3theta+i sin3theta...

    Text Solution

    |

  15. Prove that |a1alpha1+b1beta1a1alpha2+b2beta2a1alpha3+b1beta3a2alpha1+b...

    Text Solution

    |

  16. If alpha,beta,gamma are the roots of p x^3+q x^2+r=0, then the value...

    Text Solution

    |

  17. Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(...

    Text Solution

    |

  18. If |1xx^2xx^2 1x^2 1x|=, then find the value of |x^3-1 0x-x^4 0x-x^...

    Text Solution

    |

  19. If |x^n x^(n+2)x^(n+3)y^n y^(n+2)y^(n+3)z^n z^(n+2)z^(n+3)|=(x-y)(y-z)...

    Text Solution

    |

  20. Solve the system of the equations: a x+b y+c z=d a^2x+b^2y+c^2z=d^2 a^...

    Text Solution

    |