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

`lim_(xto0) |x|`

Text Solution

Verified by Experts

We see that when `xto0, |x|to0`
Let us establish this using `epsilon-delta` technique. Let `epsilongt0` we seek a `deltagt0` depending on
`epsilons.t. |x-0|epsilon implies||x|-0|let epsilon`
Now `||x|-o|=||x||=|x|ltdelta`
Choosing `epsilon=delta` we have
`|x|topsoil implies||x|-0|ltepsilon`
`therefore lim_(xto0)|x|=0`
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]

lim_(xto2) (|x|+ 3)

lim_(xto0)( x^2 + 3)

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

lim_(xto-2)[x]

Prove that lim_(xtoa) x=a

Evaluate the following lim_(xto0)((3+x)^3-27)/x

lim_(xto0) cos(1/x)

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