Question

Find whether the function f(x) = 2-|x|/x continuous at a=0​

Answer 1

Answer:

Answer is '0'

Step-by-step explanation:

The function f(x)=2 x−∣x∣ can be written as

f(x)={

2 x+x

2 x−

:

:

x≤0

x>0

.

Now,

x→0−

lim

f(x)=

x→0−

lim

3 x=0.

And,

x→0+

lim

f(x)=

x→0+

lim

x=0.

So we've,

x→0−

lim

f(x)=

x→0+

lim

f(x)=f(0).

So the function f(x) is continuous at x=0.