Can I have a clear explanation how to work these. Thank you.

1.

00 The Taylor series for at) 2 2:3 at -2 is ch($ + 2)". 1120 Find the first few coefficients. 00 The Taylor series for f(.'B) = e'E at a = 3 is 2 (1,42: 3)". n=0 Find the first few coefficients. The Maclaurin series of the function f($) = 10932623 00 can be written as x) = Z cum" 11:0 where the first few coefficients are: The Maclaurin series of the function x) 2 2:1":2 SiJ1{7;t:) 00 can be written as x) 2 2 Cum" 11:0 where a few of the coefficients are: The Maclaurin series of the function f($) = 3005(9332) 00 can be written as f($) = 2 can?" 11:0 where a few of the coefficients are: The Maclaurin series of the function at) 2 93*: tall1 (6:132) 00 can be written as f($) = 2 Cum" 11:0 where a few of the coefficients are: Suppose g is a function which has continuous derivatives, and that 9(0) 2 6, 91(0) 2 11, 9"(0) = 7 and g'"(0) = 12. What is the Taylor polnomial of degree 2 for g, centered at a = 0? W: What is the Taylor polnomial of degree 3 for g, centered at a = 0? T393] = Use T2 (at) to approximate 0-2) a S Use T3(:t':) to approximate 0-2) a E