Home
Class 12
MATHS
If f(x)=|x-2|+1 , evaluate lim(xto2+)(...

If `f(x)=|x-2|+1` , evaluate `lim_(xto2+)(f(x)-f(2))/(x-2)` and `lim_(xto2-)(f(x)-f(2))/(x-2)` . What can you say about the existence of f' (x) at x = 2 ?

Text Solution

Verified by Experts

The correct Answer is:
Therefore, f(x) is not differentiable at x = 2
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Multiple Choice Type Questions|14 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Very short Answer Type Questions|38 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE

    CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

If f(x) =|x-2|+1, evaluat Lt_(xto2+)(f(x)-f(2))/(x-2) and Lt_(xto2-)(f(x)-f(2))/(x-2) . What can you say about the existence of f'(x) at x=2?

If f(x)=|x+2|-1,"evalute "underset(x rarr-2+)(lim)(f(x)-f(-2))/(x+2)andunderset(xrarr-2-)(lim)(f(x)-f(-2))/(x+2) . What can you say about the existence of f'(x)" at"x=-2 ?

If f(2)=4,f'(2)=4 , then evalute lim_(xto2)(xf(2)-2f(x))/(x-2) .

Evaluate lim_(xto2) (x^(2)-5x+6)/(x^(2)-4).

Evaluate lim_(xto2) sin(e^(x-2)-1)/(log(x-1))

Evaluate lim_(xto-2^(+)) (x^(2)-1)/(2x+4).

If f(3)=6andf'(3)=2 , find the value of lim_(xto3)(xf(3)-3f(x))/(x-3) .

Find ("lim")_(xto2)(xf(2)-2f(x))/(x-2) if f(2)=4 and f′(2)=1

If |f(x)|lex^(2), then prove that lim_(xto0) (f(x))/(x)=0.

If f''(0)=k,kne0 , then the value of lim_(xto0)(2f(x)-3f(2x)+f(4x))/(x^2) is

CHHAYA PUBLICATION-DIFFERENTIATION-Example
  1. Given, f (x) =(x-1)/(2x^(2)-7x+5)' when x ne 1 =-(1)/(3) when...

    Text Solution

    |

  2. A function f (x) is defined as follows : f (x) = 3 + 2x , when -(...

    Text Solution

    |

  3. If f(x)=|x-2|+1 , evaluate lim(xto2+)(f(x)-f(2))/(x-2) and lim(xt...

    Text Solution

    |

  4. The function f satisfies the equation f(x+y) = f (x) f (y) for all ...

    Text Solution

    |

  5. Differentiate the following functions with respect to x : 2x^(a)-...

    Text Solution

    |

  6. Differentiate the following functions with respect to x : 2x^(4)-(...

    Text Solution

    |

  7. Differentiate the following functions with respect to x : (x^(3)-4x...

    Text Solution

    |

  8. Differentiate the following functions with respect to x : 2log(3)...

    Text Solution

    |

  9. Differentiate the following functions with respect to x : 3secx-4co...

    Text Solution

    |

  10. Differentiate the following functions with respect to x : sin2(x)/...

    Text Solution

    |

  11. Find (dy)/(dx) , when y=2^(x)x^(5)

    Text Solution

    |

  12. Find (dy)/(dx) , when y = sqrt(x) log x* 10^(x)

    Text Solution

    |

  13. Find (dy)/(dx) y= sqrt(x) sec x tan x

    Text Solution

    |

  14. If f(x+y) = f(x) * f(y) for all real x and y and f(5)=2,f'(0) = 3 ,...

    Text Solution

    |

  15. If f (a) = 2 , f'(a) = 1, g (a) = -1 and g'(a) = 2 , show tha...

    Text Solution

    |

  16. Find the derivatives of the following functions w.r.t. x : y = (si...

    Text Solution

    |

  17. Find the derivatives of the following functions w.r.t.x : y=(x^...

    Text Solution

    |

  18. Find the derivatives of the following functions w.r.t.x : (cot x + ...

    Text Solution

    |

  19. Find the derivatives of the following functions w.r.t.x : (x sin ...

    Text Solution

    |

  20. If h(x) = [ f (x) ] ^(2) + [ g (x) ] ^(2) and (x) = g (x), f''(x)...

    Text Solution

    |