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- Using the Maclaurin expansion of ?^?, sin(x)and ?n(1 + ?) find the series expansion up to the 4th non-zero term of thefollowing functions: -e^(x+1) -sin(x/2)find the first few terms of the taylor series of f(x) = 1/x at a = 1, solve by replacing x with (x-1)For 1(a) instead of using the power series representations of sin(x), cos(x) etc, you need to use the given power series representation of f(x). Please show all work
- Use the difference to find a power series representation for the function f(x)=3/(1+x)2.Plot the sine series expansion and the translation expansion for the function f(t). At f(0) for each expansion, give the value that the function converges to. f(t) = t^2 for 0 =< t < 1 f(t) = 1 for 1 =< t <2Given: f(x)=3-x, P=6 Expand the function into its cosine series representations and evaluate a2.