Home
Class 11
MATHS
Find lim(x to 1) f(x), where f(x)={{:...

Find `lim_(x to 1) f(x)`, where
`f(x)={{:(x^(2)-1,xle1),(-x^(2)-1,xgt1):}`

Text Solution

Verified by Experts

Here `f(x)={{:(x^(2)-1,xle1),(-x^(2)-1,xgt1):}`
at x=1
LHL=`underset(xrarr1^(-))"lim"f(x)`
`=underset(hrarr0)"lim"f(1-h)`
`=underset(hrarr0)"lim"(1-h)^(2)-1`
`=(1-0)^(2)-1=0`
RHL `=underset(xrarr1^(+))"lim"f(x)`
`=underset(hrarr0)"lim"-(1+h)^(2)-1`
`=-(1+0)^(2)-1=-2`
`because` LHL `ne` RHL
`therefore underset(xrarr1)"lim"f(x)` does not exist
Let `1+h=x`
`rArr 1+hrarr1`
`rArr hrarr0`
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    NAGEEN PRAKASHAN|Exercise EX -13.2|11 Videos

  • LIMITS AND DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|30 Videos

  • LIMITS AND DERIVATIVES

    NAGEEN PRAKASHAN|Exercise EX-13H|9 Videos

  • INTRODUCTION OF THREE DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|6 Videos

  • LINEAR INEQUALITIES

    NAGEEN PRAKASHAN|Exercise MISCELLANEOUS EXERCISE|14 Videos

Similar Questions

Explore conceptually related problems

lim_(x rarr1)f(x), where f(x)={x^(2)-1,x 1

Find (lim)_(x rarr1)f(x), where f(x)=[x^(2)-1,x 1

Find lim_(x to 1) f(x) , where f(x) = {{:(x + 1, x != 1),(0, x = 1):}}

Let f(x)={:{(x^(2)-1",",xle1),(-x^(2)-1",",xgt1.):} "Find"lim_(xrarr1)f(x).

Find lim_(x to 0)f(x) and lim_(x to 1)f(x) , where f(x)={{:(2x+3",", x le 0), (3(x+1)",", x gt 0):}

Find lim_(xrarr1) f(x) where f(x)= {[(x^2-1)/(x-1), x ne 1],[1, x=1]:}

Find lim_(x rarr 0) f(x) where f(x) = {(2x+3,xle0),(3(x+1),xgt0):}

Calculate lim_(x to 0) f(x) , where f(x) = (1)/(x^(2)) for x gt 0

The values of a and b if the function f(x)={{:(x^(2)+3x+a",",xle1),(bx+2",",xgt1):} is differentiable at x =1, are :