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Section 1.4 Miscellaneous

Solve the following problems:

    1. Solve the following equation: \(\pi ^{x+1}=e\text{.}\)

    2. Solve the following equation: \(2^{3^x}=10\text{.}\)

  2. 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.