German exercises for Abitur. Translate into english

Question

Please help me to translate into English the last three questions(f,g,h) from this photo. Can you give me some ideea to solve this problems?

Can you recommend me some math, physics dictionary?

Thanks!

Answer 1

f) Show that the function $F_0$ given by $$F_0(x):=4 \ln (x+1) + {4\over x+1}\qquad (x>-1)$$ is a primitive of $f_0$.

Between the graph of $f_0$ and the $x$-axis one has in the first quadrant a piece of area extending to infinity. Check whether this area is finite.

g) The function $f_1$ has to be approximated by a function $g_{c,b}$ of the form $$g_{c,b}(x):=c\cdot e^{bx}\qquad(x>-1)\ .$$ How should we choose $c$ and $b$ such that the graphs of $f_1$ and $g_{c,b}$ intersect in two points $P_1$, $P_2$ with $x_1=0$ and $x_2=1$?

h) Compute for the values $c$ and $b$ found in g) the angle between the two graphs at the intersection point $P_1$.

PS: In order to solve h) compute the slopes of the two graphs at $P_1$ and use the formula for $\tan(\alpha-\beta)$.