Home
Class 12
MATHS
If f(x)={{:(,(x log cos x)/(log(1+x^(2))...

If f(x)=`{{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):}` then

A

discontinous at zero

B

continous but not differentiable at zero

C

differentiable at zero

D

not continous and not differentiable at zero

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|30 Videos

  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise HIGHER ORDER DERIVATIVES|32 Videos

  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos

  • INTEGRATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|29 Videos

Similar Questions

Explore conceptually related problems

If f(x)={((log(1+2ax)-log(1-bx))/(x)",", x ne 0),(k",", x =0):} is continuous at x = 0, then value of k is

f(x)={{:((1-cos2x)/(x^(2)),if x ne 0),(5, if x = 0):} at x = 0 .

If f(x) = {{:((log(1+2ax)-log(1-bx))/(x)",",x ne 0),(" "k",",x = 0):} is continuous at x = 0, then k is equal to

Let f(x)={{:("sin 4x"/"log (1+3x)",","x ne 0),("A+1",","x=0):} The value of A for f to be continuous at x=0 is

If f(x)={((log(1+x)-log(1-x))/(x)"," , "when " x ne 0),(3"," , "when " x = 0):} is

If f(x) {:(=(log (1-2x)-log(1-3x))/x", " x != 0 ),(=a", " x = 0 ):} is continuous at x = 0 , then : a =

Find k, if possible, so that f (x)= [{:((ln (2- cos 2x))/(ln ^(2) (1+ sin 3x)),,, x lt 0),(k,,, x=0),((e ^(sin 2x )-1)/(ln (1+ tan 9x)),,, x gt 0):} is continious at x=0.

TARGET PUBLICATION-DIFFERENTIATION -COMPETITIVE THINKING
  1. If f:R to R is defined by f(x)={{:(,(x-2)/(x^(2)-3x+2),"if "x in R-(1,...

    Text Solution

    |

  2. If f(x) = {:{((x -1)/(2x^(2) - 7 x +5) , " for " x ne 1) , (-1/3 ...

    Text Solution

    |

  3. If f(x)={{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):} then

    Text Solution

    |

  4. For the function f(x)={{:(,|x-3|,x ge 1),(,(x^(2))/(4)-(3x)/(2)+(13)/(...

    Text Solution

    |

  5. If f(x) = x for x le 0 = 0 for x gt 0, then f(x) at x = 0 is

    Text Solution

    |

  6. At the point x = 1 , then function f(x) = {{:(x^(3) - 1, 1lt x lt o...

    Text Solution

    |

  7. Define f(x) = {{:(x^(2)+bx+c , ",",x lt 1),(x,",",x ge 1):}. If f(x) i...

    Text Solution

    |

  8. If f is differentiable at x=1, Then lim(x to1)(x^2f(1)-f(x))/(x-1) is

    Text Solution

    |

  9. if f(2)=4,f'(2)=1 then lim(x->2){xf(2)-2f(x)}/(x-2)

    Text Solution

    |

  10. If f(x) is differentiable at x=a, then lim(x toa)(x^2f(a)-a^2f(x))/(x-...

    Text Solution

    |

  11. Suppose f(x) is differentiable at x = 1 and lim(h->0) 1/h f(1+h)=5, th...

    Text Solution

    |

  12. Let f : R to R be a function defined by f(x) = max. {x, x^(3)}. The s...

    Text Solution

    |

  13. Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p ...

    Text Solution

    |

  14. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is

    Text Solution

    |

  15. If the function g(x) = {(ksqrt(x+1) " when " 0 le x le 3),(mx + 2 " ...

    Text Solution

    |

  16. Let S={t in R: f(x)=|x-pi|(e^(|x|)-1)sin|x| is not differentiable at t...

    Text Solution

    |

  17. If y=cos (2x +45^(@) ),then (dy)/(dx) =

    Text Solution

    |

  18. If y=sqrtsinsqrtx, then (dy)/(dx) =

    Text Solution

    |

  19. d/(dx)log|x|e=

    Text Solution

    |

  20. The differential coefficient of f(loge x) w.r.t. x, where f(x) = loge...

    Text Solution

    |