Home
Class 11
MATHS
If f(x)={(x^3, x gt 0),(0, x=0),(-x^3, ...

If `f(x)={(x^3, x gt 0),(0, x=0),(-x^3, x lt0):}`

A

f(x) is differentiable at x= 0

B

f(x) is continuous but not differentiable at x 0

C

Left hand derivative of f(x) at X = 0 is 1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If f(x)={(-1, xlt0 ),(0, x =0),(1, x gt 0):} and g(x)=x(1-x^2), then , f(g(x)) is continuous for,

Let g(x)=1+x-[x] and f(x)=={(-1, x lt0),(0, x=0),(1, x gt 0):} Then for all x find f(g(x))

If f(x)={(2x+3, "when x" lt 0),(0, "when x"=0),(x^2+3, "when x"gt 0):} Discuss continuity at x=0.

The function f is defined by f(x)={(,1-x,x lt 0),(,1,x=0),(,x+1,x gt 0):} Draw the graph of f(x).

Show that the signum function f:RR rarr RR , given by f(x)={(1" if "x gt 0),(0 " if "x = 0),(-1 " if " x lt0):} is neither one-one nor onto.

Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):} Discuss the continuity of f, f' on [0, 2].

Discuss the continuity of the function f, where f is defined by f(x)={{:(2x," if "x lt 0),(0," if "0 le x le 1),(4x," if "x gt 1):} .

A function f (x) is defined as follows : f (x)={{:(x,"when "xge0),(-x,"when " x lt0):} Examine the cotinuity and differentiability of (x) at x= 0 .

Show that the function f given by f(x)= {{:(x^3+3," if "x ne 0),(1," if "x=0):} is not continuous at x=0.

Let f(x) be a polynomial of degree one and f(x) be a function defined by f(x)={(g(x), x le0), ((1+x)/(2+x)^(1//x), x gt0):} If f(x) is continuous at x=0 and f(-1)=f'(1), then g(x) is equal to :

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If f(x) = sec 2x + cosec 2x, then f(x) is discontinuous at all points ...

    Text Solution

    |

  2. For a real number y, let [y] denotes the greatest integer less than or...

    Text Solution

    |

  3. If f(x)={(x^3, x gt 0),(0, x=0),(-x^3, x lt0):}

    Text Solution

    |

  4. Let h(x) = min {x, x^2}, x in R then h(x) is

    Text Solution

    |

  5. The set of all points where the functionf(x)= frac(x)(1+|x| is differe...

    Text Solution

    |

  6. Let f(x) = a+ b|x| + c|x|^4 where a, b and continuous are real constan...

    Text Solution

    |

  7. If f(x) = sqrt(1-sqrt1-x^2 , then at x = 0

    Text Solution

    |

  8. If f(x) = 2x + |x-x^2|, - 1 lex le1 then f(x) is

    Text Solution

    |

  9. Let f(x+y) = f(x) . f(y) for all x,y where f(0) ne 0. If f(5) =2 and f...

    Text Solution

    |

  10. If f is an even function such that lim(hrarr0)(f(h)-f(0))/h has some f...

    Text Solution

    |

  11. The values of constants a and b so as to make the function f(x)={(1/|x...

    Text Solution

    |

  12. If f(x)=sqrt((x-sinx)/(x+cos^2x)), then lim(x rarr infty)f(x) is

    Text Solution

    |

  13. Number of points at which f(x) = |x^2+x|+|x-1| is non-differentiable i...

    Text Solution

    |

  14. If lim(x rarr 0)(((a-n)nx-tanx)sinnx)/x^2=0, where n is non zero real ...

    Text Solution

    |

  15. lim(x rarrpi/4)(int2^(sec^2x) f(t)dt)/(x^2-pi^2/16)

    Text Solution

    |

  16. The value of lim(x rarr0)(int0^(x^2) cost^2dt)/(x sin x) is

    Text Solution

    |

  17. If f(x)=1/3{f(x+1)+5/(f(x+2)}} and f(x) gt 0 for all x in R, then lim(...

    Text Solution

    |

  18. If phi(x)=lim(nrarrinfty)(x^(2n)f(x)+g(x))/(1+x^(2n)), then

    Text Solution

    |

  19. Let f(x) = [x^3 - 3] where [.] denotes the greatest integer function T...

    Text Solution

    |

  20. If f(x)={(x[x], 0lexlt2),((x-1)[x], 2lexle3'):}, where [.] denotes the...

    Text Solution

    |