Project 1. Using the fact that |a|=a*a2, show that |a*b||a||b|. This inequality is the famous "Cauchy-Schwartz Inequality."Project 2. Use the fact that |ab|2=(ab)*(ab) to show that|ab||a||b|[ Hint: Use the Cauchy-Schwartz Inequality from Project 1, and the fact that |v|2=v*v for any vector v in Rn.]Project 3. Consider the function defined byf(x)={xy(x2-y2)x2y2,if(x,y)(0,0)0,if(x,y)=(0,0)(a) Find fx and fy for (x,y)(0,0).(b) Use the limit definition of partial derivatives to find fx(0,0) and fy(0,0).[Hint: By "limit definition" of partial derivatives, we mean:fx(a,b)=limxaf(x,b)-f(a,b)x