91Ó°ÊÓ

Asymptotes Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions. $$p(x)=\sec \left(\frac{\pi x}{2}\right), \text { for }|x|<2$$

Other techniques Evaluate the following limits, where a and \(b\) are fixed real numbers. $$\lim _{t \rightarrow a} \frac{\sqrt{3 t+1}-\sqrt{3 a+1}}{t-a}$$

Other techniques Evaluate the following limits, where a and \(b\) are fixed real numbers. $$\lim _{x \rightarrow a} \frac{x-a}{\sqrt{x}-\sqrt{a}}, a>0$$

Determine the interval(s) on which the following functions are continuous; then evaluate the given limits. $$f(x)=\frac{1+\sin x}{\cos x} ; \lim _{x \rightarrow \pi / 2^{-}} f(x) ; \lim _{x \rightarrow 4 \pi / 3} f(x)$$

Determine the end behavior of the following transcendental functions by evaluating appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist. $$f(x)=\sin x$$

We write \(\lim _{x \rightarrow a} f(x)=-\infty\) if for any negative number \(M\) there exists \(a \delta>0\) such that $$f(x) < M \quad \text { whenever } \quad 0< |x-a| < \delta$$ Use this definition to prove the following statements. $$\lim _{x \rightarrow-2} \frac{-10}{(x+2)^{4}}=-\infty$$

Asymptotes Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions. $$g(\theta)=\tan \left(\frac{\pi \theta}{10}\right)$$

Asymptotes Use analytical methods and/or a graphing utility to identify the vertical asymptotes (if any) of the following functions. $$q(s)=\frac{\pi}{s-\sin s}$$

Determine the interval(s) on which the following functions are continuous; then evaluate the given limits. $$f(x)=\frac{\ln x}{\sin ^{-1} x} ; \lim _{x \rightarrow 1^{-}} f(x)$$

Other techniques Evaluate the following limits, where a and \(b\) are fixed real numbers. $$\lim _{x \rightarrow a} \frac{x^{2}-a^{2}}{\sqrt{x}-\sqrt{a}}, a>0$$