Calculus

Taylor Series

Taylor Series Approximation

         

Let f(x)f(x) be a function such that f(0)=3,f(0)=1,f(0)=3, f'(0)=1, and f(3)=1.f(3)=1. Using a quadratic Taylor polynomial of f(x),f(x), we can approximate the value of f(0)f''(0) as f(0)AB,f''(0) \approx -\frac{A}{B}, where AA and BB are coprime integers. Find the value of AB.AB.

Using the quadratic Taylor polynomial of f(x)=1x f(x) = \frac{1}{x} at x=5, x=5, find the approximate value of 17 \frac{1}{7} multiplied by 53.5^3.

For the linear Taylor polynomial g(x)=ax+bg(x)=ax+b of f(x)=1x1f(x)=-\frac{1}{x-1} at x=2,x=2, find the error ee defined by e=23(g(x)f(x))2dx.e=\int_{2}^{3}{(g(x)-f(x))^2 dx}.

Using the quadratic Taylor polynomial of f(x)=lnx f(x) = \ln{x} at x=4, x=4, we can approximate the value of ln9 \ln{9} in the form lnA+B,\ln{A}+B, where AA and BB are rational numbers. Find the value of 2A2B. 2A^2B.

Let f(x)f(x) be a function such that f(0)=1,f(0)=2,f(0)=1, f'(0)=2, and f(3)=1.f(3)=1. Using a quadratic Taylor polynomial of f(x),f(x), we can approximate the value of f(0)f''(0) as f(0)AB,f''(0) \approx -\frac{A}{B}, where AA and BB are coprime integers. Find the value of AB.AB.

×

Problem Loading...

Note Loading...

Set Loading...