Find the Taylor series for f ( x ) centered at the given value
of a . (Assume that f has a power series expansion. Do not show
that R n ( x ) → 0 . f ( x ) = 2 /x , a = − 4
Find the Taylor polynomial of degree 2 centered at a = 1 for the
function f(x) = e^(2x) . Use Taylor’s Inequality to estimate the
accuracy of the approximation e^(2x) ≈ T2(x) when 0.7 ≤
x ≤ 1.3
(a) Determine the Taylor Series centered at a = 1 for the
function f(x) = ln x.
(b) Determine the interval of convergence for this Taylor
Series.
(c) Determine the number n of terms required to estimate the
value of ln(2) to within Epsilon = 0.0001.
Can you please help me solve it step by step.
1] Find an nth-degree polynomial function with real
coefficients satisfying the given conditions. If you are using a
graphing utility, use it to graph the function and verify the real
zeros and the given function value.
n=3;
2 and 5i are zeros;
f(1) = 52
f(x)= ?
(Type an expression using x as the variable. Simplify your
answer.)
2] Find an nth-degree polynomial function with real
coefficients satisfying the given conditions. If you are using a
graphing utility, use it...
Find an nth-degree polynomial function with real coefficients
satisfying the given conditions. If you are using a graphing
utility, use it to graph the function and verify the real zeros and
the given function value.
n= 4;
-1,4, and 4+2i are zeros
f(1)=-156
a) Find the Taylor series for sinh(x) (centered at x=0), for e^x
(centered at x=0) and hyperbolic sine and hyperbolic cosine.
b) same as a but cosh(x) instead
Using the function f(x)=ln(1+x)
a. Find the 8 degree taylor polynomial centered at 0 and
simplify.
b. using your 8th degree taylor polynomial and taylors
inequality, find the magnitude of the maximum possible error on
[0,0.1]
c.approximate ln(1.1) using your 8th degree taylor polynomial.
what is the actual error? is it smaller than your estimated
error?Round answer to enough decimal places so you can
determine.
d. create a plot of the function f(x)=ln(1+x) along with your
taylor polynomial. Based on...
A) Find the directional derivative of the function at the given
point in the direction of vector v. f(x, y) = 5 + 6x√y, (5, 4), v =
<8, -6>
Duf(5, 4) =
B) Find the directional derivative,
Duf, of the function at the given
point in the direction of vector v.
f(x, y)
=ln(x2+y2), (4, 5),
v = <-5, 4>
Duf(4, 5) =
C) Find the maximum rate of change of f at the given
point and the direction...