Could you show me the workings of this polynomial function f(x)=cos x ?
1 Answer
Dec 30, 2017
Explanation:
#"using "color(blue)"Taylor series"#
#•color(white)(x)f(x)=sum_(n=0)^oo(f^n(a))/(n!)(x-a)^n#
#=f(a)+(f'(a))/(1!)(x-a)+(f''(a))/(2!)(x-a)^2+(f'''(a))/(3!)(x-a)^3+...#
#color(orange)"Reminder"#
#d/dx(sinx)=cosx" and "d/dx(cosx)=-sinx#
#"here "a=pi/2#
#f(a)=cos(pi/2)=0#
#f'(x)=-sinxrArrf'(pi/2)=-1#
#"since linear polynomial required we can stop here"#
#rArrf(x)=0+(-1)(x-pi/2)+0#
#rArrf(x)=-(x-pi/2)larrcolor(blue)"linear polynomial"#