Home
Class 11
MATHS
Let f(x){{:((x)/(|x|)",",xne0),(0",",x=0...

Let `f(x){{:((x)/(|x|)",",xne0),(0",",x=0):}`
Show that `lim_(xrarr0)f(x)` does not exist.

Text Solution

Verified by Experts

`lim_(xto0^(+))f(x)=lim_(hto0)(0+h)=lim_(hto0)f(h)=lim_(hto0|-h|)=lim_(hto0)h/h=1" "[becausehgt0]`
`lim_(xto0^(-))f(x)=lim_(hto0)f(0-h)=lim_(hto0)(-h)/(|-h|)=lim_(hto0)(-h)/(h)=-1.`
`thereforelim_(xto0^(+))f(x)nelim_(xto0)f(x)and so limf(x)` does not exist.
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    RS AGGARWAL|Exercise EXERCISE 27B|72 Videos

  • HYPERBOLA

    RS AGGARWAL|Exercise EXERCISE 24|23 Videos

  • LINEAR INEQUATIONS (IN ONE VARIABLE)

    RS AGGARWAL|Exercise EXERCISE 6B|12 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={{:((|x|)/(x)",",xne0),(2",",x=0.):} Show that lim_(xrarr0)f(x) does not exist.

Let f(x)={:{((3x)/(|x|+2x)',xne0),(0",",x=0.):} Show that lim_(xrarr0)f(x) does not exist.

Show that lim_(xrarr0)e^(-1//x) does not exist.

Show that lim_(xrarr0)1/x does not exist.

Let f(x)={{:((|x-3|)/((x-3))",",xne3),(0",",x=3.):} Show that lim_(xrarr3)f(x) does not exist.

Show that lim_(xrarr0)sin""(1)/(x) does not exist.

Show that (lim)_(x rarr0)(x)/(|x|) does not exist.

If f(x)={{:((x-|x|)/(x)","xne0),(2", "x=0):}, show that lim_(xto0) f(x) does not exist.

Let f(x)={{:(1+x^(2)",",0lexle1),(2-x",",xgt1.):} Show that lim_(xrarr0)f(x) does not exist.

Let f(x)={:{((|x|)/(x)",",xne0),(0",",x=0.):} Find lim_(xrarr0)f(x).