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 ENGLISH|Exercise Multiple correct answers type|11 Videos
  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If f(a)=2 f'(a)=1 g(a)=-1 g'(a)=2 then lim_(xtoa)(g(x)f(a)-g(a)f(x))/(x-a) is

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)_(xvec0)(((dy)/(dz)))/x

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) and g(x) = (1)/(x^(3)) . Then the value of (f(x)+g(x))/(f(-x)-g(-x)) at x = 2 is

If f(4)=g(4)=2 , f^(prime)(4)=9,g^(prime)(4)=6, then (lim)_(xto4)(sqrt(f(x))-sqrt(g(x)))/(sqrt(x)-2) is equal to (a) 3sqrt(2) b. 3/(sqrt(2)) c. 0 d. does not exists

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

If f^(prime)(1)=-2sqrt(2) and g^(prime)(sqrt(2))=4 , then the derivative of f(tanx) with respect to g(secx) at x=pi/4, is: (a)1 (b) -1 (c) 2 (d) 4

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

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

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If y^2=P(x), then 2d/dx(y^3(d^2y/dx^2))

    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. Let y=(2^((log)2 1/4x)-3^((log)(27) (x^2+1)^3-2x))/(7^(4(log)(49)x)-...

    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 >0, prove that([1+((dy)/(dx))^2]^(...

    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 df(n)=5040. Then the valu...

    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, show that (d^2y)/(dx^2)=((dy)/(dx))^2

    Text Solution

    |

  19. If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a and tany/2=sqrt((...

    Text Solution

    |

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

    Text Solution

    |