Home
Class 12
MATHS
Let f(x) = |x-1|+|x+1| Discuss the conti...

Let `f(x) = |x-1|+|x+1|` Discuss the continuity and differentiability of the function.

Text Solution

Verified by Experts

The correct Answer is:
`x = +- 1`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 2|4 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = x|x| for all x in R . Discuss continuity and derivability of f(X) at x = 0

If f(x) = (x^(2)-1)/(x-1) Discuss the continuity at x rarr 1

If f(x) = {|x|-|x-1|}^(2) , draw the graph of f(x) and discuss its continuity and differentiability of f(x)

Discuss the continuity of f(x) = tan^(-1)x

Draw the graph of the function and discuss the continuity and differentiability at x = 1 for, f(x) = {{:(3^(x)",","when",-1 le x le 1),(4-x",","when",1 lt x lt 4):}

Let f(x) = xe^-(1/|x|+1/x); x != 0, f(0) = 0 , test the continuity & differentiability at x = 0

The function f(x) = |x| + |x-1| + |x-2| is continuous but not differentiable at for all x in R x=-1 and x=1

Draw the graph of the function f(x) = x - |x - x^(2)|, -1 le x le 1 and discuss the continuity or discontinuity of f in the interval -1 le x le 1

Discuss the continuity and differentiability for f(x) = [sin x] when x in [0, 2pi] , where [*] denotes the greatest integer function x.

Let f(x)={{:(x sin.(1)/(x)",",x ne0),(0",",x=0):}} and g(x)={{:(x^(2)sin.(1)/(x)",", x ne 0),(0",", x=0):}} Discuss the graph for f(x) and g(x), and evaluate the continuity and differentiabilityof f(x) and g(x).

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let f(x) = |x-1|+|x+1| Discuss the continuity and differentiability of...

    Text Solution

    |

  2. For every pair of continuous function f, g : [0, 1] rarr R such that m...

    Text Solution

    |

  3. Let f: R to R and g:R to R be respectively given by f(x) =|x|+1 and g...

    Text Solution

    |

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

    Text Solution

    |

  5. Q. For every integer n, leta(n) and b(n) be real numbers. Let functio...

    Text Solution

    |

  6. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R. a. ...

    Text Solution

    |

  7. If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...

    Text Solution

    |

  8. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  9. If lim(xtooo)((x^(2)+x+1)/(x+1)-ax-b)=4, then

    Text Solution

    |

  10. Let fandg be real valued functions defined on interval (-1,1) such tha...

    Text Solution

    |

  11. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

    Text Solution

    |

  12. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

    Text Solution

    |

  13. Fill in the blank, in the statement given below. Let f(x) = x|x The ...

    Text Solution

    |

  14. lf is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, th...

    Text Solution

    |

  15. The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|...

    Text Solution

    |

  16. The left hand derivative of f(x) = [x] sin (pi x)"at x" = k is an inte...

    Text Solution

    |

  17. Which of the following functions is differentiable at x = 0 ?

    Text Solution

    |

  18. For x in R, f(x) =|log(e) 2-sinx| and g(x) = f(f(x)) , then

    Text Solution

    |

  19. If the function g(X) ={{:( ksqrt ( x+1), 0 le x le 3),( mx+2, 3 lt x...

    Text Solution

    |

  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

    Text Solution

    |

  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

    Text Solution

    |