Miscellaneous

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Section 1.4 Miscellaneous

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Solve the following problems:

1. Solve the following equation: $\pi ^{x+1}=e\text{.}$
2. Solve the following equation: $2^{3^x}=10\text{.}$
Find the domain of the function $f(x)=\frac{\ln (\ln (\ln x))}{x-3}+\sin x\text{.}$
1. What is meant by saying that $L$ is the limit of $f(x)$ as $x$ approaches $a\text{?}$
2. What is meant by saying that the function $f(x)$ is continuous at $x=a\text{?}$
3. State two properties that a continuous function $f(x)$ can have, either of which guarantees the function is not differentiable at $x=a\text{.}$ Draw an example for each.