All Tasks - Asymptote

Calculate the derivative for $f(x)=3e^x$ and $g(x)=e^{x^2}$ and give the answer for $f'(2)$ and $g'(2)$. Round to three decimal places.

The velocity of a stone sinking in a lake is given by \begin{equation}v(t)=2.5\cdot(1-e^{-0.1\cdot t})\end{equation} with $t$ in seconds and $v(t)$ in $\frac{m}{s}$. How fast is the stone sinking at the beginning? How fast after ten seconds? Round to three decimal places, if needed.

In the table above you can see the basketball results of the four children- namely Lena, Angeló, Marie and Juan. Which of them has the best scoring rate and it’s therefore the best player of the game? Tick the right name!

Determinate the intersection point of the two linear functions: $f(x)=-1,5x-1\\ g(x)=3x+8$.

Let $f(x)=xe^x$. Which $x\in\mathbb{R}$ solves the equation $f'(x)-f(x)=0$?

Let the function $f(x)=\frac{e^x+x}{e^x}$, we can say that