Question

if f''(x)= -cos(x)+sin(x), and f(0)=1 and f(pi)=), what is the original function

Answer #1

Find the Taylor series for the function f(x)=sin(pi(x)-pi/2)
with center a=1

Prove that the family of trigonometric functions { 1, cos x, sin
x, ..., cos nx, sin nx, ...} form an orthogonal system on [-pi,pi]
prove that the following orthogonality relations
hold integral from -pi to pi of sin nx dx = 0 and integral from
-pi to pi of cos nx dx = 0

1) find the
absolute extrema of function f(x) = 2 sin x + cos 2x on the
interval [0, 2pi]
2)
is f(x) = tanx
concave up or concave down at x = phi / 6

fourier expansion, piecewise function.
f(x){ pi , -1<x<0
-pi , 0<x<1

what is the derivative of the f in dirction of the original
let f(x, y) =sin (xy^2) at (pi, -1)

Find f.
a. f '''(x) = cos x, f(0) = 1, f '(0) = 4, f ''(0) = 3
b. f''(x) = sin(x) + cos (x), f(0) = 1, f'(0) = 3.

Consider the function on the interval (0, 2π). f(x) = sin(x)
cos(x) + 4. (A) Find the open interval(s) on which the function is
increasing or decreasing. (Enter your answers using interval
notation.) (B) Apply the First Derivative Test to identify all
relative extrema.

Find the Fourier series of the function:
f(x) =
{0, -pi < x < 0
{1, 0 <= x < pi

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

1. Find the area between the curve f(x)=sin^3(x)cos^2(x) and y=0
from 0 ≤ x ≤ π
2. Find the surface area of the function f(x)=x^3/6 + 1/2x from
1≤ x ≤ 2 when rotated about the x-axis.

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