Question

(1 point) Let F(x)=∫o,x sin(6t^2) dt F(x)=∫0xsin(6t^2) dt. The
integrals go from 0 to x

Find the MacLaurin polynomial of degree 7 for F(x)F(x).

Use this polynomial to estimate the value of ∫0, .790 sin(6x^2) dx
∫0, 0.79 sin(6x^2) dx. the integral go from 0 to .790

Answer #1

Consider the function f(x)=x⋅sin(x).
a) Find the area bound by y=f(x) and the x-axis over the interval,
0≤x≤π. (Do this without a calculator for practice and give the
exact answer.)
b) Let M(x) be the Maclaurin polynomial that consists of the
first 5 nonzero terms of the Maclaurin series for f(x). Find M(x)
by taking advantage of the fact that you already know the Maclaurin
series for sin x.
M(x)=
c) Since every Maclaurin polynomial is by definition centered at...

Let f(x, y) = sin x √y.
Find the Taylor polynomial of degree two of f(x, y) at (x, y) =
(0, 9).
Give an reasonable approximation of sin (0.1)√ 9.1 from the
Taylor polynomial of degree one of f(x, y) at (0, 9).

a). Find dy/dx for the following integral.
y=Integral from 0 to cosine(x) dt/√1+ t^2 ,
0<x<pi
b). Find dy/dx for tthe following integral
y=Integral from 0 to sine^-1 (x) cosine t dt

Let h be the function defined by H(x)= integral pi/4 to x
(sin^2(t))dt. Which of the following is an equation for the line
tangent to the graph of h at the point where x= pi/4.
The function is given by H(x)= integral 1.1 to x (2+ 2ln( ln(t) ) -
( ln(t) )^2)dt for (1.1 < or = x < or = 7). On what
intervals, if any, is h increasing?
What is a left Riemann sum approximation of integral...

Explain whether the following integrals converge or not. If the
integral converges, find the value. If the integral does not
converge, describe why (does it go to +infinity, -infinity,
oscillate, ?)
i) Integral from x=1 to x=infinity of x^-1.4 dx
ii) Integral from x=1 to x=infinity of 1/x^2 * (sin x)^2 dx
iii) Integral from x=0 to x=1 of 1/(1-x) dx

Let F = (sin(x 3 ), 2yex 2 ). Evaluate the line integral Z C F ·
dr, where C consists of two line segments, which go from (0, 0) to
(2, 2), and then from (2, 2) to (0, 2).

1. Evaluate the definite integral given
below.
∫(from 0 to π/3) (2sin(x)+3cos(x)) dx
2. Given F(x) below, find F′(x).
F(x)=∫(from 2 to ln(x)) (t^2+9)dt
3. Evaluate the definite integral given
below.
∫(from 0 to 2) (−5x^3/4 + 2x^1/4)dx

Let w(x,y,z) = x^2+y^2+z^2 where x=sin(8t), y=cos(8t) , z=
e^t
Calculate dw/dt by first finding dx/dt, dy/dt, and dz/dt and using
the chain rule
dx/dt =
dy/dt=
dz/dt=
now using the chain rule calculate
dw/dt 0=

Let f(x)=sin x-cos x,0≤x≤2π
Find all inflation point(s) of f.
Find all interval(s) on which f is concave downward.

f is an integral from 0 to x^2
x*sin(pi*x)
for x > 0
calculate f(35)

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