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Using only ANALYTICAL (algebraic) methods

Using only ANALYTICAL (algebraic) methods (i.e. don't just make a table of values or just look at the graph), determine the following limits, if they exist. (think Calculus 1)

a. \(\lim _{x \rightarrow b} \frac{\frac{1}{x}-\frac{1}{b}}{x-b}\)

b. \(\lim _{x \rightarrow-2} \frac{\sqrt{x+3}-1}{x+2}\)

c. \(\lim _{x \rightarrow-\infty} \frac{3 x+1}{\sqrt{2 x^{2}+4}}\)

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Answer #1

Here i am using simplification of given function and then apply limit to that function .

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