Home
Class 12
MATHS
The function f(x)=sin^(-1)(cosx) is disc...

The function `f(x)=sin^(-1)(cosx)` is discontinuous at `x=0` (b) continuous at `x=0` (c) differentiable at `x=0` (d) none of these

Text Solution

Verified by Experts

Given that,
`f(x)=sin^(-1)(cosx)`
`f(x)=sin^(-1)(sin(pi/2-x))`
`f(x)=pi/2-x`
`implies` function is continuous and differentiable at `x=0`
Hence, option (b) and (c) both are correct.
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    RD SHARMA|Exercise Solved Examples And Exercises|403 Videos

  • DIFFERENTIAL EQUATION

    RD SHARMA|Exercise Solved Examples And Exercises|634 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=sin^(-1)(cos x) is discontinuous at x=0 continuous at x=0 differentiable at x=0 non of these

The function f(x)=1+|cos x| is (a) continuous no where ( b ) continuous everywhere (c) not differentiable at x=0 (d) not differentiable at x=n pi,n in Z

Show that the function f(x)={x^(m)sin((1)/(x))0,x!=0,x=0 is differentiable at x=0 if m>1 continuous but not differentiable at x=0, if 0.

If the function f(x)=(sin10 x)/x , x!=0 is continuous at x=0 , find f(0) .

1.If lim_(x rarr0)(f(x))/(x) exists and f(0)=0 then f(x) is (a) continuous at x=0 (b) discontinuous at x=0 (e) continuous no where (d) None of these

Let f : R rarr R satisfying l f (x) l <= x^2 for x in R, then (A) f' is continuous but non-differentiable at x = 0 (B) f' is discontinuous at x = 0 (C) f' is differentiable at x = 0 (D) None of these

Show that the function f(x)={x sin((1)/(x)) when x!=0;=0, when x=0 is continuous butnot differentiable at x=0

Show that the function f(x)={x^(m)sin((1)/(x)),x!=00,quad x=0 is continuous but not differentiable at x=0, if @

If f(x) ={ (x.ln(cosx))/ln (1+x^2) x!=0 , 0, x=0 then a) f is continuous at x =0 b) f is continuous at x =0 but not differentiable at x=0 c) f is differemtiable at x =0 d) f is not continuous at x =0

The function f(x)=e^(-|x|) is continuous everywhere but not differentiable at x=0 continuous and differentiable everywhere not continuous at x=0 none of these

RD SHARMA-DIFFERENTIABILITY-Solved Examples And Exercises
  1. If f(x)=sqrt(x^2+9) , write the value of (lim)(x->4)(f(x)-f(4))/(x-4) ...

    Text Solution

    |

  2. Let f(x)=|x| and g(x)=|x^3| , then f(x) and g(x) both are continuous a...

    Text Solution

    |

  3. The function f(x)=sin^(-1)(cosx) is discontinuous at x=0 (b) continuou...

    Text Solution

    |

  4. The set of points where the function f(x)=x|x| is differentiable i...

    Text Solution

    |

  5. If f(x)={(|x+2|)/(tan^(-1)(x+2)),\ \ \ x!=-2 2,\ \ \ \ \ \ \ \ \ \ \ \...

    Text Solution

    |

  6. Let f(x)=|x| . Then, for all x f is continuous (b) f is differentiabl...

    Text Solution

    |

  7. The function f(x)=e^(|x|) is (a) Continuous everywhere but not differ...

    Text Solution

    |

  8. The function f(x)=|cosx| is (a) everywhere continuous and differe...

    Text Solution

    |

  9. If f(x)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1...

    Text Solution

    |

  10. If f(x)=a|sinx|+b\ e^(|x|)+c\ |x|^3 and if f(x) is differentiable at x...

    Text Solution

    |

  11. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)++(x^2)/((1+x^2)^n)+ , then...

    Text Solution

    |

  12. If f(x)=|(log)e x| , then (a) f'(1^+)=1 (b) f^'(1^(-))=-1 (c) f'...

    Text Solution

    |

  13. If f(x)=|(log)e|x| , then f(x) is continuous and differentiable for...

    Text Solution

    |

  14. Let f(x)={(1/(|x|), for |x| ge 1),(ax^2+b,for |x| < 1)) . If f(x) is c...

    Text Solution

    |

  15. The function f(x)=x-[x] , where [] denotes the greatest integer fun...

    Text Solution

    |

  16. Let f(x)={a x^2+1,\ \ \ \ \ x &gt;1 , \ \ \ \ x+1//2,\ \ \ \ \ xlt=1 ...

    Text Solution

    |

  17. Let f(x)=|sinx| . Then, (a) f(x) is everywhere differentiable. ...

    Text Solution

    |

  18. Let f(x)=|cosx| . Then, f(x) is everywhere differentiable (b) f(x) ...

    Text Solution

    |

  19. The function f(x)=1+|cosx| is (a) continuous no where (b) continuou...

    Text Solution

    |

  20. The function f(x)=|cosx| is differentiable at x=(2n+1)\ pi//2,\ \ n in...

    Text Solution

    |