LHpitals Rule Determine which of the following limits can be evaluated using LHpitals
Chapter 8, Problem 65(choose chapter or problem)
L’Hôpital’s Rule Determine which of the following limits can be evaluated using L’Hôpital’s Rule. Explain your reasoning. Do not evaluate the limit.
(a) \(\lim _{x \rightarrow 2} \frac{x-2}{x^{3}-x-6}\)
(b) \(\lim _{x \rightarrow 0} \frac{x^{2}-4 x}{2 x-1}\)
(c) \(\lim _{x \rightarrow \infty} \frac{x^{3}}{e^{x}}\)
(d) \(\lim _{x \rightarrow 3} \frac{e^{x^{2}}-e^{9}}{x-3}\)
(e) \(\lim _{x \rightarrow 1} \frac{\cos \pi x}{\ln x}\)
(f) \(\lim _{x \rightarrow 1} \frac{1+x(\ln x-1)}{(x-1) \ln x}\)
Text Transcription:
lim_x rightarrow 2 x-2/x^3-x-6
lim_x rightarrow 0 x^2-4x/2x-1
lim_x rightarrow infinity x^3/e^x
lim_x rightarrow 3 e^x^2-e^9/x-3
lim_x rightarrow 1 cos pi x/ln x
lim_x rightarrow 1 1+x(ln x-1)/(x-1)ln x
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