{Use of Tech} Small argument approximations Consider the following common approximations when x is near zero. 


b. Estimate f(0.2) and give a bound on the error in the approximation.


f(x) = sin ⁻¹ x ≈ x

Taylor series and interval of convergence

b. Write the power series using summation notation.

f(x) = cosh 3x, a = 0

{Use of Tech} Small argument approximations Consider the following common approximations when x is near zero. 

b. Estimate f(0.2) and give a bound on the error in the approximation.

f(x) = tan x ≈ x

Taylor series and interval of convergence

a. Use the definition of a Taylor/Maclaurin series to find the first four nonzero terms of the Taylor series for the given function centered at a.

b. Write the power series using summation notation.

f(x) = 1/x², a=1

{Use of Tech} Small argument approximations Consider the following common approximations when x is near zero. 

b. Estimate f(0.2) and give a bound on the error in the approximation.

f(x) =√(1+x) ≈ 1 + x/2

Taylor series

b. Write the power series using summation notation.

f(x)=sin x, a = π/2

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

b. Let f(x)=x⁵−1 The Taylor polynomial for f of order 10 centered at 0 is f itself.