Home
Class 12
MATHS
If f(x)={{:(x","" "xlt0),(1","" "x=0),(x...

If `f(x)={{:(x","" "xlt0),(1","" "x=0),(x^(2)","" "xgt0):}," then find " lim_(xto0) f(x)"` if exists.

Text Solution

Verified by Experts

The correct Answer is:
0
We have `underset(xto0^(-))limf(x)=underset(xto0)limx=0`
and `underset(xto0^(+))limf(x)=underset(xto0)limx^(2)=2`
Hence, `underset(xto0)limf(x)` is equal `" to "0.`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.2|7 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise EXERCISE 2.3|15 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Solved Examples|15 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

Let f(x)={{:(cos[x]", "xle0),(|x|+a", "xgt0):}. Then find the value of a, so that lim_(xto0) f(x) exists, where [x] denotes the greatest integer function less than or equal to x.

Letf(x)={{:(x+1,", "if xge0),(x-1,", "if xlt0):}".Then prove that" lim_(xto0) f(x) does not exist.

IF f(x)={{:(x,"if",x,"is rational"),(1-x,"if",x, "is irrational"):},"then find" lim_(xto1//2) f(x) if exists.

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

Let f(x){:(=1,",""for "xgt0),(=x^(2),",""for "xle0):} ,discuss whether underset(xrarr0)"lim"f(x) exists or not .

If f(x)=|{:(sinx,cosx,tanx),(x^(3),x^(2),x),(2x,1,x):}| , then lim_(xto0)(f(x))/(x^(2))=

Let f(x)={{:(1+(2x)/(a)", "0lexlt1),(ax", "1lexlt2):}."If" lim_(xto1) "f(x) exists, then a is "

Let f (x) ={{:((sin pix)/(5x) ",","when " x ne0),(K",", "when" x=0):} If lim _(xto0) lim f(x) =f(0), then the value of K is-

f(x)={x ,xlt=0 1,x=0,t h e nfin d("lim")_(xvec0)f(x)x^2,x >0ife xi s t s