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0 1 ,0 , forms Evaluate the following limits. Check your
Chapter 4, Problem 40RE(choose chapter or problem)
\(1^{\infty},\ 0^0,\ \infty^0\) forms Evaluate the following limits. Check your results by graphing.
\(\lim _{x \rightarrow \infty}\ x^{1/x}\)
Questions & Answers
QUESTION:
\(1^{\infty},\ 0^0,\ \infty^0\) forms Evaluate the following limits. Check your results by graphing.
\(\lim _{x \rightarrow \infty}\ x^{1/x}\)
ANSWER:Solution Step 1 1/x In this problem we have to evaluate limx By direct substitution of limit, we get lim x 1/x= 1/ = 0 x 1/x 0 Thus lx has the indeterminate form . To evaluate this limit we will be using the following two steps: g(x) 0, Assume limf(x) has the indeterminate form 0 1 , . 0 xa 0 1. Evaluate L = lixax)ln f(x).This limit can often be put in the form 0or both of which can be handled by l’hopital’s rule. g(x) 2. Then limf(x) = eL xa l'Hôpital's Rule: f(x) 0 f(x) ± Suppose that we have one of the following cases, lim xa g(x)= 0r lixa g(x) ± Where a can be any real number, infinity or negative infinity. f(x) f(x) In these cases we have lim g(x)= lim gx) xa xa