Study questions...need to know how for exam
I have a set of problems that I don't know how to do. I'm using them to study for my exam, so please show a step-by-step or at least a basic idea how to do it.
1) $\displaystyle \int^5_1 \frac{log_5 x}{x}dx$
2) Evaluate: $\displaystyle lim_{x \to 0} (\frac{1}{ln(x+1)} - \frac{1}{x})$
3) Californium-252 has a half-life of 2.645 years. If the equation describing the decay of the readioactive nuclei is given by $\displaystyle y=y_0e^{kt}$, find:
a) the value of k
b) how long it will take for 95% of the radioactive nuclei to disintegrate.
4) Solve:$\displaystyle \frac{dy}{dx} + y = x$
I don't even know what I'm supposed to do on this one...(Wondering)
5) $\displaystyle \int x^3e^xdx$
6) Use $\displaystyle \frac{dy}{dx} = ky(M-y)$ with k=.001 and M=150 to write y as a function of t. $\displaystyle (y_o = 5)$
Thank you!!!