For each problem, be sure to show all work to explain your answers. Part of your grade is clearly communicating how you arrive at your answer. While you may use a calculator to check your answers, any explanation should NOT involve a calculator.

You will need to upload ONE file with all your answers to all the questions written on it$.$

$(14\mathrm{.}3)$ Show that the limit does not exist by showing $2$ different limits along $2$ different paths approaching the point: $\underset{(x,y)(0,0)}{lim}\frac{3y^2}{x^2+5y^2}$

$(14\mathrm{.}4)$ Find an equation of the tangent plane to the surface $f(x,y)=ycosx$ at the point $(\frac{}{3},2).($Be sure to show work for finding the relevant partial derivatives and use exact values$).$