Home
Class 12
MATHS
lim(xto0)|x|/x...

`lim_(xto0)|x|/x`

Text Solution

Verified by Experts

L.H.L.`=lim_(xto0-)|x|/x`
`=lim_(hto0)([0-h])/(0-h)=lim_(hto0)h/(-h)=-1`
R.H.L.`=lim_(xto0+)([x])/x=lim_(hto0)([0+h])/(|0+h|)=1`
As `L.H.L.neR.H.L.,`
So the limit does not exist.
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|88 Videos

  • LINEAR INEQUALITIES

    MBD PUBLICATION|Exercise QUESTION BANK|46 Videos

Similar Questions

Explore conceptually related problems

lim_(xto0)7

lim_(xto0)[x]

Evaluate the following: lim_(xto0)(x^(1/2)+2x+3x^(3/2))/(2x^(1/2)-2x^(5/2)+4x^(7/2))

Examine the existence of the following limits: lim_(xto0-)e^(1/x)

Examine the existence of the following limits: lim_(xto0+)e^(1/x)

lim_(xto-2)[x]

lim_(xto2) (|x|+ 3)

lim_(xto1)|x^2-3x+2|/(x^2-3x+2)

Using the epsilon- delta definition prove that lim_(xto2)|5x -7| = 3

Using the epsilon- delta definition prove that lim_(xto1)|3x +2| = 5