Home
Class 12
MATHS
Let fandg be real valued functions defin...

Let `fandg` be real valued functions defined on interval `(-1,1)` such that `g''(x)` is constinous, `g(0)=0`, `g'(0)=0,g''(0)=0andf(x)=g(x)sinx`.
Statement I `lim_(xrarr0)(g(x)cotx-g(0)cosecx)=f''(0)`
Statement II `f'(0)=g'(0)`

A

Both statement I and Statement II are correct and Statement II is the correct explanation of Statement I

B

Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I

C

Statement I is correct but Statement II is incorrect

D

Statement II is correct but Statement I is incorrect.

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|15 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|64 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

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

Similar Questions

Explore conceptually related problems

Let f and g be real valued functions defined on interval (-1,\ 1) such that g"(x) is continuous, g(0)!=0 , g'(0)=0, g"(0)!=0 , and f(x)=g(x)sinx . Statement-1 : ("Lim")_(x->0)[g(x)cotx-g(0)"c o s e c"x]=f"(0) and Statement-2 : f'(0)=g(0)

Let f and g be real valued functions defined on interval (-1, 1) such that g'' (x) is continuous, g(0) ne 0, g'(0) = 0, g''(0) ne 0, and f(x) = g''(0) ne 0 , and f(x) g(x) sin x . Statement I lim_( x to 0) [g(x) cos x - g(0)] [cosec x] = f''(0) . and Statement II f'(0) = g(0).

f(0)=0=g(0) and f'(0)=6=g'(0)thenlim_(x rarr0)(f(x))/(g(x))=

If (x)={x,x 0 and g(x)=f(x)+|x| then lim_(x rarr0^(+))(log_(|sin x|)x)^(g(x))=

Find lim_(x rarr 0.4)( f(x)- f(0.4))/(g(x)-g(0.4))

Statement I if f(0)=a,f'(0)=b,g(0)=0,(fog)'(0)=c then g'(0)=(c)/(b). Statement II (f(g(x))'=f'(g(x)).g'(x), for all n

Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) g(x), x ne 0 If g(0)=g'(0)=0 and f(x) is continuous at x=0, then f'(0) is

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