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Calculus 2: Applications of Taylor polynomials

Complete the square for the expression x22x+3x^2 - 2x + 3 and rewrite it in the form ab2a - b^2.

Look at the Taylor polynomial for cos(x)\cos(x) and we're cutting it off at degree 4, T4(x)T_4(x). We want to figure out what values of xx you can plug in there for it to be accurate to two decimal places.

Using a Taylor polynomial, approximate a function when x is in the range [7,upper bound][7, \, \text{upper bound}].

Find the fourth degree Taylor polynomial for the function f(x)=lnxf(x) = \ln x centered at c=1c = 1 and use it to approximate ln(1.1)\ln(1.1).