Home
Class 11
MATHS
Show that lim(xrarr0)e^(-1//x) does not ...

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

Text Solution

Verified by Experts

Let `f(x)=e^(-1//x).`Then,
`lim_(xto0^(+))f(x)=lim_(hto0)f(0+h)=lim_(hto0)f(h)=lim_(hto0)e^(-1//1)=lim_(hto0)(1)/(e^(1//h))=(1)/(oo)=0.`
`lim_(xto0)f(x)=lim_(hto0)f(0-h)=lim_(hto0)f(-h)=lim_(hto0)e^(1//h)=oo." "[becausee^(oo)=oo]`
`because lim_(xto0^(-))f(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),(0",",x=0):} Show that lim_(xrarr0)f(x) does not exist.

Let f(x)={{:((|x|)/(x)",",xne0),(2",",x=0.):} Show that lim_(xrarr0)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)={:{((3x)/(|x|+2x)',xne0),(0",",x=0.):} Show that lim_(xrarr0)f(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.

If f(x)=(|x|)/(x) , then show that lim_(xrarr0) f(x) does not exist.

If f(x) is defined as follows: f(x){{:(1,x,gt0),(-1,x,lt0),(0,x,=0):} Then show that lim_(xrarr0) f(x) does not exist.

Show that (lim)_(x rarr0)(1)/(2) does not exist.

Show that lim_(xrarr2)(x)/([x]) does not exist.