The Taylor series for f(x)=ln⁡(sec⁡(x))\displaystyle {f{{\left({x}\right)}}}={\ln{{\left({\sec{{\left({x}\right)}}}\right)}}} at a=0\displaystyle {a}={0} is ∑n=0∞cn(x)n.\displaystyle {\sum_{{{n}={0}}}^{\infty}}{c}_{{n}}{\left({x}\right)}^{{n}}.
Find the first few coefficients.

c0=\displaystyle {c}_{{0}}=  
c1=\displaystyle {c}_{{1}}=  
c2=\displaystyle {c}_{{2}}=  
c3=\displaystyle {c}_{{3}}=  
c4=\displaystyle {c}_{{4}}=  

Find the exact error in approximating ln⁡(sec⁡(0.2))\displaystyle {\ln{{\left({\sec{{\left({0.2}\right)}}}\right)}}} by its fourth degree Taylor polynomial at a=0.\displaystyle {a}={0}.
The error is  

License