Question

lim x tends to 0 (x²)/|x|​

Answer 1

Answer: The question is related to Limits and continuity

We have: lim x tends to 0  (x²)/|x|

Step-by-step explanation:

Step-1 : modulas of x i.e,|x| is a signum function

So it has two values

|X|= +x for x>0

      -x for x<0

We will use

Lim x tends to 0+ (x²)/|x|

Which is equal to   (x²)/+x

As x tends to zero the term will be equal to lim x tends to 0+  0/0 form

In that case we use L-hospitals rule

Differentiate numerator and denominator seperately w.r.t x we get

Lim x tends to 0+   2X/1

The answer is 0

Now lim x tends to 0- (x²)/|x|

Lim x tends to 0- (x²)/-x

Same rule applies here as well

So answer is 0 again

Now lim x tends to 0 (x²)/|x| = 0

Which implies that limit of the function exists..