Find the quadratic approximating polynomial for the function f(x)= cos x centere

Question

Find the quadratic approximating polynomial for the function f(x)= cos x centered at a=0. use the approximation to estimate the value of cos 01. Please solve fully.

Explanation / Answer

5th root (256)/ 6th root(64) = 2^x First convert any of the roots on the LHS to whole numbers if that is possible: => 256^(1/5) / 2= 2^x Multiply both sides by 2: => 256^(1/5) = 2*(2^x) Take logs of both sides; => log [ 256^(1/5)] = log [ 2(2^x)] By log indices law: => (1/5) log 256 = x log 2 + log 2 Subtract log 2 from both sides: => [ (1/5) log 256 ] - log 2 = x log 2 Divide both sides by log 2: => x = [ [(1/5) log 256] - log 2 ] / log 2 Simplify: => x = [ [(1/5) log 256]/ log 2 ] - 1 Evaluate with a calculator: => x = 0.6

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