Section+7.7+–+Indeterminate+Form+and+L’Hopital’s+Rule+–+Homework

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=Evaluate the limit (a) without using L’Hopital’s (b) using L’Hopital’s Rule.=

math \displaystyle \textbf{1)} \large \begin{equation} \lim_{x\to 3} \tfrac{2(x-3)}{x^2-9} \end{equation} math

math \displaystyle \textbf{2)} \large \begin{equation} \lim_{x\to 3} \tfrac{\sqrt{x+1}-2}{x-3} \end{equation} math

math \displaystyle \textbf{3)} \large \begin{equation} \lim_{x\to 0} \tfrac{\sin (4x)}{2x} \end{equation} math

math \displaystyle \textbf{4)} \large \begin{equation} \lim_{x\to \infty} \tfrac{5x^2-3x+1}{3x^2-5} \end{equation} math

math \displaystyle \textbf{5)} \large \begin{equation} \lim_{x\to 0} \tfrac{e^x-(1-x)}{x} \end{equation} math

math \displaystyle \textbf{6)} \large \begin{equation} \lim_{x\to 0} \tfrac{\sin (2x)}{\sin(3x)} \end{equation} math

math \displaystyle \textbf{7)} \large \begin{equation} \lim_{x\to \infty} \tfrac{3x^2-2x+1}{2x^2+3} \end{equation} math

=(a) Describe the type of indeterminate form (if any) that is obtained by direct substitution.= =(b) Evaluate the limit using L'Hopital's Rule if necessary.= =(c) Using the applet explain how the graph verifies you results.=

math \displaystyle \textbf{8)} \large \begin{equation} \lim_{x\to 0^+} (-x \ln(x)) \end{equation} math media type="custom" key="25870218"

math \displaystyle \textbf{9)} \large \begin{equation} \lim_{x\to \infty} x \tan(\tfrac{1}{x}) \end{equation} math media type="custom" key="25870358"

math \displaystyle \textbf{10)} \large \begin{equation} \lim_{x\to \infty} (1+\tfrac{1}{x})^x \end{equation} math media type="custom" key="25888220"

math \displaystyle \textbf{11)} \large \begin{equation} \lim_{x\to 2^+} (\tfrac{8}{x^2-4}-\tfrac{x}{x-2}) \end{equation} math media type="custom" key="25888272"

math \displaystyle \textbf{12)} \large \begin{equation} \lim_{x\to 0^+} (\tfrac{10}{x}-\tfrac{3}{x^2}) \end{equation} math media type="custom" key="25888302"