Home
Class 11
MATHS
If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prim...

If `f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2,` then the value of `lim_(x->a)(g(x)f(a)-g(a)f(x))/(x-a)` is (a)`-5` (b) `1/5` (c) `5` (d) none of these

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If f(a) = 2, f'(a) = 1, g(a) = -1 and g'(a) = 2 , find the value of lim_(x rarr a)(g(x)f(a) - g(a)f(x))/(x-a)

If f (a) =2, f '(a) =1, g (a) =-3 .g'(a) =-1 , then the value of lim _(xtoa)(f(a) g(x) -g(a)f(x))/(a-x) is equal to-

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of lim_(x->0)(((dy)/(dz)))/x

If f (a) = 2 , f'(a) = 1, g (a) = -1 and g'(a) = 2 , show that lim_(x to a)(g(x)f(a)-f(x)g(a))/(x-a) = 5

If lim_(xtoa)[f(x)+g(x)]=2 and lim_(xtoa) [f(x)-g(x)]=1, then find the value of lim_(xtoa) f(x)g(x).

If f(x)={(x^2+2,,,xge2),(1-x ,,,xlt2):} ; g(x)={(2x,,,xgt1),(3-x ,,,xle1):} then the value of lim_(x->1) f(g(x)) is

If the function f(x)=x^(3)+e^((x)/(2)) and g(x)=f^(-1)(x) , then the value of g'(1) is

If f(x) is an invertible function and g(x)=2f(x)+5, then the value of g^(-1)(x)i s

If f(x) = [x] and g(x)=|x| the value of f(g(8/5))-g(f(-8/5)) is

If f(x)=xtan^(-1)x , find f^(prime)(sqrt(5)) .

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If y^2=P(x), where P(x) is a polynomial of degree 3, then 2d/dx(y^3(d^...

    Text Solution

    |

  2. If g(x)=|(f(x+c),f(x+2c),f(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(...

    Text Solution

    |

  3. If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of li...

    Text Solution

    |

  4. If x=a(cost+tsint) and y=a(sint-tcost), find (d^2y)/(dx^2)

    Text Solution

    |

  5. Prove that (2^((log)2 1/4x)-3^((log)(27)(x^2+1)^3)-2x) /(7^(4(log)(49...

    Text Solution

    |

  6. (lim)(hvec0)((e+h)^(1n(e+h))-e)/hi s

    Text Solution

    |

  7. If (x-a)^(2)+(y-b)^(2)=c^(2), for some c gt 0, prove that ([1+((dy)/...

    Text Solution

    |

  8. if y=(x^2-1)^m , then the (2m)th differential coefficient of y is

    Text Solution

    |

  9. If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prim...

    Text Solution

    |

  10. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

    Text Solution

    |

  11. If y=e^(acos^(-1)x),-1lt=x<1,s how t h a t (1-x^2)(d^2y)/(dx^2)-x(dy)...

    Text Solution

    |

  12. Let f(x)=(x-1)(x-2)(x-3)...(x-n),n in N ,a n d f'(n)=5040. Then the v...

    Text Solution

    |

  13. If y=((a x+b))/((x^2+c)) , then find dy/dx .

    Text Solution

    |

  14. If y=xlog"{"x/((a+b x))"}" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

    Text Solution

    |

  15. y=f(x), where f satisfies the relation f(x+y)=2f(x)+xf(y)+ysqrt(f(x)),...

    Text Solution

    |

  16. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 ...

    Text Solution

    |

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

    Text Solution

    |

  18. If e^y(x+1)=1, prove that (d^2y)/(dx^2)=((dy)/(dx))^2

    Text Solution

    |

  19. y=tan^(-1) ((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)) show that dy/d...

    Text Solution

    |

  20. If y=cos^(-1)(cosx),then (dy)/(dx) at x=(5pi)/4 is equal to (a)1 (b)-...

    Text Solution

    |