Answer:
a) 
b) See Below for proper explanation
Step-by-step explanation:
a) The objective here is to Use the power series expansions for ex, sin x, cos x, and geometric series to find the first three nonzero terms in the power series expansion of the given function.
The function is 
The expansion is of
is 
The expansion of cos x is 
Therefore; ![e^x + 3 \ cos \ x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ... 3[1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...]](https://tex.z-dn.net/?f=e%5Ex%20%2B%203%20%5C%20cos%20%5C%20x%20%20%3D%201%20%2B%20%5Cdfrac%7Bx%7D%7B1%21%7D%2B%20%5Cdfrac%7Bx%5E2%7D%7B2%21%7D%2B%20%5Cdfrac%7Bx%5E3%7D%7B3%21%7D%20%2B%20...%203%5B1%20-%20%5Cdfrac%7Bx%5E2%7D%7B2%21%7D%2B%20%5Cdfrac%7Bx%5E4%7D%7B4%21%7D-%20%5Cdfrac%7Bx%5E6%7D%7B6%21%7D%2B%20...%5D)

Thus, the first three terms of the above series are:

b)
The series for
is 
let consider the series; 

Thus it converges for all value of x
Let also consider the series 
It also converges for all values of x
Answer:
10
Step-by-step explanation:
You can get the three consecutive integers by using <em>algebraic expressions.</em>
Let's solve.
Let x be the <u>smallest even integer</u>.
Let x+2 be the second even integer.
Let x+4 be the largest even integer.
- x =

Therefore, 10 is the smallest even integer.
x+2 = 10+2 = 12
The second even integer is 12.
x+4 = 10+4 = 14
The largest even integer is 14.
Let's check by adding the three even integers.
10+12+14 = 36
36 = 36
<em>It's correct. </em>
I tried calculating the problem but couldn't seem to find an answer. I checked on my graphics calculator and on the computer and they provide a "No Solution" answer. The steps shown above lead to a dead end in the calculation.
you just add them together to get 17