Question

Evaluate the following limit or explain why it does not exist.\\ $\lim_{x \to 0} (20x + \cos x)^{\frac{1}{x}}$ Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.\ A. $L = \lim_{x \to 0} \frac{1}{x} \ln(20x + \cos x)$ is finite and therefore $\lim_{x \to 0} (20x + \cos x)^{\frac{1}{x}}$ can be written as the expression (Type an expression using L as the variable.)\ This implies that $\lim_{x \to 0} (20x + \cos x)^{\frac{1}{x}} = $ (Type an exact answer in simplified form.)\ B. The limit does not exist because it has the indeterminate form $\infty^0$ which cannot be written in the form $\frac{0}{0}$ or $\frac{\infty}{\infty}$ so that l'Hôpital's rule can be applied.\ C. The limit does not exist because it has the indeterminate form $0^0$ which cannot be written in the form $\frac{0}{0}$ or $\frac{\infty}{\infty}$ so that l'Hôpital's rule can be applied.\ D. The limit does not exist because it has the indeterminate form $1^\infty$ which cannot be written in the form $\frac{0}{0}$ or $\frac{\infty}{\infty}$ so that l'Hôpital's rule can be applied.

          Evaluate the following limit or explain why it does not exist.\\
$\lim_{x \to 0} (20x + \cos x)^{\frac{1}{x}}$
Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.\
A. 
$L = \lim_{x \to 0} \frac{1}{x} \ln(20x + \cos x)$ is finite and therefore $\lim_{x \to 0} (20x + \cos x)^{\frac{1}{x}}$ can be written as the expression  (Type an expression using L as the variable.)\
This implies that $\lim_{x \to 0} (20x + \cos x)^{\frac{1}{x}} = $ (Type an exact answer in simplified form.)\
B. The limit does not exist because it has the indeterminate form $\infty^0$ which cannot be written in the form $\frac{0}{0}$ or $\frac{\infty}{\infty}$ so that l'Hôpital's rule can be applied.\
C. The limit does not exist because it has the indeterminate form $0^0$ which cannot be written in the form $\frac{0}{0}$ or $\frac{\infty}{\infty}$ so that l'Hôpital's rule can be applied.\
D. The limit does not exist because it has the indeterminate form $1^\infty$ which cannot be written in the form $\frac{0}{0}$ or $\frac{\infty}{\infty}$ so that l'Hôpital's rule can be applied.

Evaluate the following limit or explain why it does not exist.

limx → 0 (20x + cos x)^(1)/(x)
Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.A.
L = limx → 0(1)/(x)ln(20x + cos x) is finite and therefore limx → 0 (20x + cos x)^(1)/(x) can be written as the expression (Type an expression using L as the variable.)This implies that limx → 0 (20x + cos x)^(1)/(x) = (Type an exact answer in simplified form.)B. The limit does not exist because it has the indeterminate form ∞^0 which cannot be written in the form (0)/(0) or (∞)/(∞) so that l'Hôpital's rule can be applied.C. The limit does not exist because it has the indeterminate form 0^0 which cannot be written in the form (0)/(0) or (∞)/(∞) so that l'Hôpital's rule can be applied.D. The limit does not exist because it has the indeterminate form 1^∞ which cannot be written in the form (0)/(0) or (∞)/(∞) so that l'Hôpital's rule can be applied.

Added by Jaime S.

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