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If your friend is getting interviews but not getting job offers, what two things would you advise them to do?

Solve the separable differential equation \[\frac{dy}{dx}=e^{x-y}\] with initial value \(y0)=0\).

If \[f(x,y)=\frac{\arcsin{y}}{x}+10x^3+xy^2+\ln(2),\] find \(\displaystyle \frac{\partial f}{\partial y}\).

Which of the following is an example of a logistic differential equation?

Let \[g(x,y,z) = 3xy + x^2 – z\] where \(x = u + v\), \(y = 2uv + w^3\), and \(z = u – vw^2\). Which of the following gives the correct formula for \(\frac{\partial g}{\partial w}\)?

Compute the area between the curves \(y=\cos^2(x)\) and \(y=1\) for \(0\leq x \leq \pi\). Hint: The following trigonometric formulas may be useful. \[\sin^2{x}+\cos^2{x}=1 \\ \sin^2{x}=\frac12(1-\cos(2x)) \\ \cos^2{x}=\frac12(1+\cos(2x))\]

Determine whether the telescopic series is convergent or divergent. If it is convergent, find the sum.\[\sum_{n=3}^\infty \dfrac{3}{n^2 +7n + 12}\]

What is a mutual fund?

What is preferred stock?

Explain why a frameshift mutation often is more serious than a point mutation.