Taylors and mclaurins theorem derive the taylors theorem

Question

Taylor's and McLaurin's theorem

i.

a. Derive the Taylor's theorem (1716)

b. Use the Taylor's theorem to expand sin (∏/6+h)

ii.

a. Derive McLaurin's theorem

b. Use the McLaurin's theorem to expand ln (x +x) in ascending powers of x as far as the term in x5.