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\centerline{MATH 133 -- Calculus with Fundamentals 1}
\centerline{More on Indeterminate Forms and Algebraic Evaluation of Limits}
\centerline{October 6, 2015}
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\noindent
{\it Background}
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Today we will work on more examples of algebraic methods to compute indeterminate
form limits. \emph{You will need to recognize which algebraic methods apply and work through examples 
like these without the prompts from me for this week's problem set and quiz.}  
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\noindent
{\it Questions}
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\noindent
Compute the following limits:
\begin{enumerate}
\item[(1)]
$$\displaystyle{\lim_{x\to 3} \frac{x^2 - 6x + 9}{x^2 - 5x + 6}},$$ 
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\item[(2)]
$$\lim_{t\to 0} \frac{3^{2t} - 1}{3^t - 1}$$
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\item[(3)] 
$$\lim_{x\to 3} \frac{x - 3}{\sqrt{x} - \sqrt{6 - x}}.$$
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\item[(4)]  
$$\lim_{x\to 0} \frac{\cot(x)}{\csc(x)}$$
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\item[(5)]
$$\lim_{x\to 2} \frac{\frac{1}{x^3} - \frac{1}{8}}{x - 2}$$
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\item[(6)]  The following one is called an $\infty - \infty$ form.  Start by putting the terms over a common
denominator. What kind of indeterminate form do you have now? Then try to apply one of the ideas we have discussed.
$$\lim_{x \to -1} \left(\frac{1}{x+1} - \frac{2}{x^2 + 4x + 3}\right).$$
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