APFIVE What is the correct sequence of steps for evaluating $$\lim_{x\to2} f(g(x))$$? Assume $$g(x)$$ is continuous and $$f(x)$$ has a removable discontinuity at the value of $$\lim_{x\to2} g(x)$$.
Evaluate $$\lim_{x\to2} g(x)$$, Factor and cancel in $$f(x)$$ if necessary, Substitute the limit, Conclude the composite limit
Factor and cancel factors in $$f(x)$$ if necessary, Evaluate $$\lim_{x\to2} g(x)$$, Substitute the limit into $$f(x)$$, Conclude the composite limit
Evaluate $$\lim_{x\to2} g(x)$$, Substitute this limit into $$f(x)$$, Factor and cancel factors in $$f(x)$$ if necessary, Conclude the value of $$\lim_{x\to2} f(g(x))$$
Substitute $$\lim_{x\to2} g(x)$$ into $$f(x)$$, Evaluate $$\lim_{x\to2} g(x)$$, Factor and cancel in $$f(x)$$, Conclude the composite limit
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