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Question

Determine the value of 'k' for which the following function is continuous at x=3,
f(x)=(x+3)236x3,x3k,x=3

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Solution

Since, the function f(x) is continuous at x=3.

Therefore,
k=limx 3(x+3)236x3
k=limx 3(x+3)262x3
k=limx 3(x+36)(x+3+6)x3
k=limx 3(x3)(x+9)x3
k=limx 3(x+9)
k=3+9=12

Hence, this is the answer.

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