Numerical approximations (no error estimates)

With the help of Taylor polynomials, approximately compute the following values (you can omit error estimates):

Variant 1
\(\sin 0.1\)
Resolution
\(\sin x = 1 - {x^3}{3!} + R_4(x)\), where \(R_4(x)\) is the remainder of the Taylor polynomial. If we assume that this remainder is small, we obtain \[ \sin 0.1 \approx 0.1 - 0.000167 = 0.09983. \] But if we wanted to know how accurate our approximation is, we would need to estimate the error \(R_4(x)\).
Variant 2
\(\cos 0.1\)
Result
\(0.995004\)
Variant 3
\(\sqrt {0.98}\)
Result
\(0.989949\)
Variant 4
\(\root 3 \of 1729.03\)
Result
\(12.00238\)
Variant 5
\(e^{0.01}\)
Result
\(1.01005\)
Variant 6
\(\log 1.2\)
Result
\(0.18232\)
Variant 7
\(1.01^{8}\)
Result
\(1.0829\)