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Find the value of k that makes f(x) continuous at x = 4

Find the value of k that makes f(x) continuous at x = 4-example-1
User Mjyazdani
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1 Answer

4 votes

Given:

The function is continuous at x = 4,


f(x)=\begin{cases}(2x^2-8x)/(x-4),x\\e4 \\ k\text{ ,x= 4}\end{cases}

As the given function is continous at x = 4,


\begin{gathered} \lim _(x\to4)f(x)=k \\ \lim _(x\to4)((2x^2-8x)/(x-4))=k \\ \lim _(x\to4)((2x(x-4))/(x-4))=k \\ \lim _(x\to4)(2x)=k \\ 2(4)=k \\ k=8 \end{gathered}

Answer: k = 8

User Keston
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