3
X2
Ex.11 If f(x) =
(
xº +X-16x+20
(x-2)2
k,
is continuous for all values of x, then the value of k is-
x=2
(3) 7
(2) 6
(1) 5
(4) 8
Answers
Answered by
2
Answer:
The given function is continuous at x=2.
Therefore,
lim
x→2
−
f(x)=lim
x→2
+
f(x)=f(2)
lim
x→2
=f(2)
Now, consider lim
x→2
f(x)=lim
x→2
(x−2)
2
x
3
+x
2
−16x+20
=lim
x→2
(x−2)
2
(x+5)(x−2)
2
=lim
x→2
(x+5)=7
Therefore,
7=f(2)=k
Hence, the required value of k is 7.
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