Question

Detumine the value of k' for which
following
function is
continuous at
x = 3 :
f(x) = {(x+3)²-36/x-3,x is not equal to 3
k,x=3



​

Answer 1

Answer:

Since f(x) is continuous at x=3.

Therefore,

x→3

lim

f(x)=f(3)

x→3

lim

f(x)=k

x→3

lim

x−3

x

2

−9

=k

x→3

lim

x−3

(x+3)(x−3)

=k

x→3

lim

(x+3)=k

k=6

Step-by-step explanation:

Since f(x) is continuous at x=3.

Therefore,

x→3

lim

f(x)=f(3)

x→3

lim

f(x)=k

x→3

lim

x−3

x

2

−9

=k

x→3

lim

x−3

(x+3)(x−3)

=k

x→3

lim

(x+3)=k

k=6