Home
Class 12
MATHS
Two functions f & g have first & second ...

Two functions f & g have first & second derivatives at x=0 & satisfy the relations, `f(0) = 2/(g(0)), f'(0)=2g'(0) = 4g(0), g"(0)= 5 f"(0)=6f(0) = 3` then-

A

If`h(x)=(f(x))/(g(x)),` then `h'(0)=15`

B

If `k(x)=f(x).g(x).sinx` then `k'(0)d=2`

C

`underset(xrarr0)lim(g'(x))/(f'(x))=(1)/(2)`

D

None of above

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise EXAMPLE|3 Videos
  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise SOLVED EXAMPLES|7 Videos
  • DIFFERENTIAL EQUATION

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos
  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is

Let f, g and h are differentiable functions. If f(0) = 1; g(0) = 2; h(0) = 3 and the derivatives of theirpair wise products at x=0 are (fg)'(0)=6;(g h)' (0) = 4 and (h f)' (0)=5 then compute the value of (fgh)'(0) .

f(x) and g(x) are two differentiable functions in [0,2] such that f"(x)=g"(x)=0, f'(1)=2, g'(1)=4, f(2)=3, g(2)=9 then f(x)-g(x) at x=3/2 is

Let f(x) be a nonzero function whose all successive derivative exist and are nonzero. If f(x), f' (x) and f''(x) are in G.P. and f (0) = 1, f '(0) = 1 , then -

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

A twice differentiable function f(x)is defined for all real numbers and satisfies the following conditions f(0) = 2; f'(0)--5 and f"(0) = 3 . The function g(x) is defined by g(x) = e^(ax) + f (x) AA x in R , where 'a' is any constant If g'(0) + g"(0)=0 . Find the value(s) of 'a'

A twice differentiable function f(x)is defined for all real numbers and satisfies the following conditions f(0) = 2; f'(0)--5 and f '' (0) = 3 . The function g(x) is defined by g(x) = e^(ax) + f (x) AA x in R , where 'a' is any constant If g'(0) + g''(0)=0 . Find the value(s) of 'a'

If f and g are two functions having derivative of order three for all x satisfying f(x)g(x)=C (constant) and (f''')/(f')-"A" (f'')/f -(g''')/(g')+(3g")/g=0 . Then A is equal to

If f(x), g(x) be twice differentiable function on [0,2] satisfying f''(x)=g''(x) , f'(1)=4 and g'(1)=6, f(2)=3, g(2)=9, then f(x)-g(x) at x=4 equals to:- (a) -16 (b) -10 (c) -8