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1) Evaluate the following derivatives.

a) LaTeX: frac{d}{dx}left(2^{2x^3}right)


b) LaTeX: frac{d}{dx}left(cosh5xright)


c) LaTeX: frac{d}{dx}left(2tanh^{-1}sqrt[]{x}right)


2) Evaluate the following integrals.

a) LaTeX: int^{e^3}_{e^2}frac{dx}{xlnxln^2left(ln xright)}






b) LaTeX: intfrac{10^{frac{1}{p}}}{p^2}dp

c) LaTeX: intfrac{dx}{xsqrt[]{1+x^4}}








3) Evaluate the given definite integral and use Theorem 7.7 from your book to express your answer in terms of logarithms.

LaTeX: int^{ln9}_{ln5}frac{cosh x}{4-sinh^2x}dx

4) Use l’Hopital’s Rule to evaluate LaTeX: lim_{xlongrightarrowinfty}frac{1-coth x}{1-tanh x}




5) Uranium-238 has a half-life of 4.5 billion years. Geologists find a rock containing a mixture of U-238 and lead, and they determine that 85% of the original U-238 remains; the other 15% has decayed into lead. How old is the rock?

6) According to the 2014 national population projections published by the U.S. Census Bureau, the U.S. population is projected to be 334.4 million in 2020 with an estimated growth rate of 0.79% per year. Assuming the growth rate remains constant, find the projected population in 2050.

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