Home
Class 12
MATHS
Let f : R rarr R satisfying |f(x)|le x^(...

Let `f : R rarr R` satisfying `|f(x)|le x^(2), AA x in R`, then show that f(x) is differentiable at x = 0.

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

Let R rarr R be a function such that f(x+y) = f(x)+f(y) AA x, y in R . If f(x) is differentiable at x= 0, then

Let f: R->R satisfying |f(x)|lt=x^2,AAx in R be differentiable at x=0. Then find f^(prime)(0)dot

If f : R rarr R is defined by f(x)=1/(2-cos3x) for each x in R , then the range of f is

A function f : R to R is defined by f(x) =x^(2) .Then show that f is neither nor surfection .

Let f:R to R be given by f(x) =|x^(2)-1|, x in R . Then

A function f : R to R satisfies the equation f(x + y) = f(x), f(y) for all x, y in R , f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f' (0) = 2. Find (f'(x))/f(x)

A function f:R rarr R satisfies the equation f(x+y)=f(x)f(y) for all x,y in R , f(x) ne 0 . Suppose that the function is differentiable at x=0 and f'(0)=2. Prove that f'(x)=2f(x).

If f : R to R is defined by f (x) =x ^(2) - 3x + 2, find f (f (x)).

A function f: R->R satisfies the equation f(x+y)=f(x)f(y) for all x , y in R and f(x)!=0 for all x in Rdot If f(x) is differentiable at x=0a n df^(prime)(0)=2, then prove that f^(prime)(x)=2f(x)dot

Show f:R rarr R defined by f(x)= x^2 + x for all x in R is many one.

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let f : R rarr R satisfying |f(x)|le x^(2), AA x in R, then show that ...

    Text Solution

    |

  2. Find x where f(x) = max {sqrt(x(2-x)),2-x} is non-differentiable.

    Text Solution

    |

  3. Discuss the differentiability of function f(x)=x-|x-x^2|

    Text Solution

    |

  4. Discuss the differentiability of f(x)="sin"|x|

    Text Solution

    |

  5. Discuss the continuity and differentiablity of f(x)=|x+1|+|x|+|x-1|...

    Text Solution

    |

  6. Discuss the differentiability of f(x)="max"{tan^(-1)x ,cot^(-1)x}dot

    Text Solution

    |

  7. find the values of a and b , such that f(x) ={ax^2+1,xle1 and x^2+ax...

    Text Solution

    |

  8. Discuss the differentiability of f(x)=|x[x]| ,-1 < x <= 2

    Text Solution

    |

  9. find the values of a and b , such that f(x) ={ax^2+1,xle1 and x^2+ax...

    Text Solution

    |

  10. Discuss the differentiability of f(x)=cos^(-1)((1-x^2)/(1+x^2))

    Text Solution

    |

  11. Which of the following function is non-differentiable in domain? (a)f(...

    Text Solution

    |

  12. Discuss the continuity of f(x)={1/(e^(x-1)),x!=1; 0,x=1

    Text Solution

    |

  13. Which of the following functions is not continuous AAx in R ?

    Text Solution

    |

  14. Find the value of f(0) so that the function. f(x)=(sqrt(1+x)-1+x^3)/x ...

    Text Solution

    |

  15. If the function f(x)={((x^2-(A+2)x+A)/(x-2), "for" x ne 2),(2, "for"...

    Text Solution

    |

  16. If the function f: R- {0}-> R given by f(x)=1/x-2/(e^(2x)-1) is conti...

    Text Solution

    |

  17. L e t f(x)=(1-tanx)/(4x-pi),x!=pi/4,x in [0,pi/2], Iff(x)i s continuou...

    Text Solution

    |

  18. If f(x)=(tan(pi/4+(log)e x))^((log)x e) is to be made continuous at x=...

    Text Solution

    |

  19. f(x)={(2xtanx-pi/(cosx) ,, x!=pi/2),(k ,, x=pi/2):} i s \ c o n t i n ...

    Text Solution

    |

  20. Discuss the continuity of f(x) ={{:(((x^(2))/|x|,xne0),(0,x=0):}

    Text Solution

    |

  21. Let f(x)={(1+3x)^(1/x), x != 0e^3,x=0 Discuss the continuity of f(x) a...

    Text Solution

    |