Question

Evaluate the left hand and right hand limit of function defined by () =

{

1 −

2

, 0 ≤ ≤ 1

2 + , > 1

at = 1.​

Answer 1

Answer:

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Step-by-step explanation:

ANSWER

Left hand limit:

x→1

lt

f(x)

=

x→1

lt

1+x

2

[∵f(x)=1+x

2

when x≤1]

=1+1

=2

Right hand limit

x→1

+

lt

f(x)

=

x→1

lt

2−x [∵f(x)=2−x when x>1]

=1

Since,

x→1

−

lt

f(x)



=

x→1

+

lt

f(x),

x→1

lt

f(x) does not exist.