Can somebody please answer this question for me?

Consider the function f(x)=xsin(x). 1. Compute limx0f(x) using l'Hpital's rule from calculus. 2. Use Taylor's remainder theorem to get the same result: (a) Write down P1(x), the first-order Taylor polynomial for sin(x) centered at a=0. (b) Use your knowledge of the derivatives of sin(x) and the fact that sin(x),cos(x)1 to show that R1(x)/x=o(1) as x0 (i.e., that limx0R1(x)/x=0 ). (c) Express f(x) as f(x)=xP1(x)+xR1(x), and compute the limits of the two terms as x0