Taylor polynomials of concrete functions

Write Taylor polynomials at 0 (e.g. of degree 5) for the following functions.

Variant 1
\(e^x\)
Result
\[1 + \frac{x^1}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \frac{x^5}{5!}.\]
Variant 2
\(\ln(x+1)\)
Result
\[x - \frac{x^2}2 + \frac{x^3}3 - \frac{x^4}4 + \frac{x^5}5.\]
Variant 3
\(\sin x\)
Result
\[ x - \frac{x^3}{3!} + \frac{x^5}{5!}. \]
Variant 4
\(\cos x\)
Result
\[1 - \frac{x^2}{2!} + \frac{x^4}{4!}.\]
Variant 5
\((1 + x)^a\)
Result
\[1 + \binom{a}1 x + \binom{a}2 x^2 + \binom{a}3 x^3 + \binom{a}4 x^4 + \binom{a}5 x^5. \]