Home
Class 12
MATHS
Let f and g be real valued functions def...

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)`

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statemcnt-2 is True, Statement-2 is Not a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Some New Pattern Problems

    A DAS GUPTA|Exercise Exercise|137 Videos

  • Screening Tests

    A DAS GUPTA|Exercise Exercise|38 Videos

  • Total Conditional Probability and Bayes' Theorem

    A DAS GUPTA|Exercise Exercise|29 Videos

Similar Questions

Explore conceptually related problems

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)

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).

Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g(x),x 0} Find g(x) such that f(x) is continuous and f'(1)=f(-1)

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

If for a continuous function f,f(0)=f(1)=0,f'(1)=2 and g(x)=f(e^(x))e^(f(x)) then g'(0)=

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

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

If f and g are derivable function of x such that g'(a)ne0,g(a)=b" and "f(g(x))=x," then 'f'(b)=

Let f and g be differentiable on R and suppose f(0)=g(0) and f'(x) =0. Then show that f(x) =0

A DAS GUPTA-Some New Pattern Problems-Exercise
  1. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

    Text Solution

    |

  2. Consider the system of equations ax + by = 0; cx + dy = 0, where a, b,...

    Text Solution

    |

  3. Let f and g be real valued functions defined on interval (-1,\ 1) such...

    Text Solution

    |

  4. Match the integrals in Column I with the values in Column II and indi...

    Text Solution

    |

  5. In the following [x] denotes the greatest integer less than for equal ...

    Text Solution

    |

  6. Match the statement in Column I with the properties in Column II and ...

    Text Solution

    |

  7. Consider the following linear equations ax+ by+cz=0, bx+ cy+az=0, cx+ ...

    Text Solution

    |

  8. Let (x,y) be such that sin-1 (ax) + cos ^-1 (y) + cos ^-1 (bxy)=pi/2...

    Text Solution

    |

  9. Let f(x) =(x^2-6x +5) / (x^2 -5x +6) Match the statement in Column I w...

    Text Solution

    |

  10. Consider the lines give by L1: x+3y -5=0, L2:3x - ky-1=0, L3: 5x +2y ...

    Text Solution

    |

  11. Consider all possible permulations of letter of the word ENDEANOEL.

    Text Solution

    |

  12. Text Solution

    |

  13. Match the statements/expressions given in Column I with the values giv...

    Text Solution

    |

  14. Match the statements/expressions given in Column I with the values giv...

    Text Solution

    |

  15. Match the statements/expressions given in Column I with the values giv...

    Text Solution

    |

  16. Match the statements/expressions given in Column I with the values giv...

    Text Solution

    |

  17. Match the statements/expressions given in Column I with the values giv...

    Text Solution

    |

  18. Let (x, y, z) be points with integer coordinates satisfying the system...

    Text Solution

    |

  19. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

    Text Solution

    |

  20. The centres of two circles C1 and C2, each of unit radius are at a dis...

    Text Solution

    |