02] Find the value of k if the following functions are continuous at given point, a) f(x) = (10 ^ x - 5 ^ x - 2 ^ x + 1)/(x ^ 2) if x=\=0 at x = 0; =klog 2, if x = 0
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Answer:
As f(x) is continuous at x=2
lim
x→2
+
f(x)=lim
x→2
+
(3x−1)
=3×2−1=6−1=5
And lim
x→2
−
f(x)=lim
x→2
−
(2x+1)
=2×2+1=4+1=5
⇒f(2
−
)=f(2
+
)=k since f is continuous at x=2
∴k=5
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