The answers to the questions
Answer:


Step-by-step explanation:
<u>Taylor series</u> expansions of f(x) at the point x = a

This expansion is valid only if
exists and is finite for all
, and for values of x for which the infinite series converges.






Substituting the values in the series expansion gives:

Factoring out e⁴:
![e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right]](https://tex.z-dn.net/?f=e%5E%7B4x%7D%3De%5E4%5Cleft%5B1%2B4%28x-1%29%2B8%7D%28x-1%29%5E2%2B...%5Cright%5D)
<u>Taylor Series summation notation</u>:

Therefore:

Answer:
Check the explanation
Step-by-step explanation:
kindly check the attached image below to Determine whether the given set S is a subspace of the vector space <u><em>(which is contained within a different vector space. So all the subspace is a kind of vector space in their own way, although it is also defined relative to some of the other larger vector space. The linear subspace is more often than not simply called a subspace whenever the situation serves to differentiate it from other types of subspaces.)</em></u> V.A
Answer:
1
Step-by-step explanation:
h