Find kk such that the following matrix M

Sketch grapf of f(y)=y for dy\dt = ay+by^2,a>0,b>0,y>0 

Evaluate the following limit ( IE do not use L'Hopital's rule).

lim𝑥→4 sin(𝑥2−4𝑥)  sin(𝑥2−10𝑥+24) .$$\underset{x\to 4}{lim}{\displaystyle \frac{\sin (x^2-4x)}{\sin (x^2-10x+24)}}.$$

A penny of mass 3.1 g rests on a small 29.1 g block supported by a spinning disk of radius 8.3 cm. The coefficients of friction between block and disk are 0.742 (static) and 0.64 (kinetic) while those for the penny and block are 0.617 (static) and 0.45 (kinetic).

$U$ is a random variable that follows Uniform distribution with interval $(0,1). X_1,...,X_n$ follows Bernoulli distribution with mean $U$. How do I find the function $f:(0,1{)}^n->R$ that minimizes $E\left[\right(U-f(X_1,...,X_n){)}^2\left)\right]$ ? I have no idea where to start solving. Thank you in advance.