Question

Discuss the continuity of f(x) at x=c:
(2x + 5 if XS2
(i) f(x) =
2'
4x+1 if x>2°C = 2​

Answer 1

Answer:

The given function is f(x)={

kx

2

,ifx≤2

3,ifx>2

The given function f is continuous at x=2

x→2

lim

f(x)=

x→2

lim

f(x)=f(2)

⇒

x→2

lim

(kx

2

)=

x→2

lim

(3)=4k

⇒k⋅2

2

=3=4k

⇒4k=3=4k

⇒4k=3

⇒k=

4

3

Therefore, the required value of k is

4

3

.