Home
Class 12
MATHS
If 3-((x^(2))/(12))lef(x)le3+((x^(3))/(9...

If `3-((x^(2))/(12))lef(x)le3+((x^(3))/(9))` in the neighborhood of x=0, then find the value of `lim_(xto0) f(x).`

Text Solution

Verified by Experts

According to question,
`underset(xto0)lim(3-(x^(2))/(12))leunderset(xto0)limf(x)leunderset(xto0)lim(3+(x^(3))/(9))`
or `(3-0)leunderset(xto0)limf(x)le(3+0)`
Hence, `underset(xto0)limf(x)=3" "`(Using sandwich theorem)
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise Solved Examples|15 Videos
  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.1|10 Videos
  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos
  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE PUBLICATION|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Find the value of lim_(xto3^(-)) (x-2)/(x-3).

The value of lim_(xto0+)(x)/(p)[(q)/(x)] is

Find the value of lim_(xto0^(+)) (sinx)^((1)/(x)) .

Evaluate lim_(xto0) (logcosx)/(x)

If f(3)=6andf'(3)=2 , find the value of lim_(xto3)(xf(3)-3f(x))/(x-3) .

Evaluate lim_(xto0) (sinx-x)/(x^(3)).

If |f(x)|lex^(2), then prove that lim_(xto0) (f(x))/(x)=0.

If (x^(2)+x-2)/(x+3)le(f(x))/(x^(2))le(x^(2)+2x-1)/(x+3) holds for a certain interval containing the value of lim_(xto-1) f(x).

Evaluate lim_(xto0) (e^(x)-1-x)/(x^(2)).

The value of lim_(x to 0)(1+3x)^((x+2)/(x)) is -