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Question
f(x) = `{{:((2^(x + 2) - 16)/(4^x - 16)",", "if" x ≠ 2),("k"",", "if" x = 2):}` at x = 2
Solution
We have, f(x) = `{{:((2^(x + 2) - 16)/(4^x - 16)",", "if" x ≠ 2),("k"",", "if" x = 2):}`
Since, f(x) is continuous at x = 2
∴ f(2) = `lim_(x -> 2) "f"(x)`
∴ k = `lim_(x -> 2) (2^(x + 2) - 16)/(4^x - 16)`
= `lim_(x -> 2) (4(2^x - 4))/((2^x - 4)(2^x + 4))`
= `lim_(x -> 2) 4/(2^x + 4)`
= `4/(4 + 4)`
= `1/2`
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