Question

Find *f*(*x*).

*f* '''(*x*) = sin *x*, *f*(0) = 1,
*f* '(0) = 2, *f* ''(0) = 3

Answer #1

1a.) Find the linearization of the function f(x) = (sin x+1)^2
at a = 0.
1b.) Differentiate the two functions below.
f(x) = ln(e^x - sin x) ; g(x) = e^-x^2

1. Let ?(?)=8(sin(?))? find f′(2).
2. Let ?(?)=3?sin−1(?) find f′(x) and f'(0.6).

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.

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.

f(x) = − cos(x^2 ) + 2 sin(x) [1,3.5]
1) find f'(x) and the roots on the given interval.
2) find all critical points of f(x) on the given interval.
3) find absolute max and min of f(x) on the given interval.

(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

1- For the following functions, find all critical numbers
exactly.
f(x) = x − 2 sin x for −2π < x < 2π
f(x) = e^−x −e^−3x for x > 0
f(x) = x^5 − 2x^3

If f(x) = sin(x^6), find the value of (f^(42))*0.

(a) Find the Riemann sum for
f(x) = 3
sin(x), 0 ≤ x ≤
3π/2,
with six terms, taking the sample points to be right endpoints.
(Round your answers to six decimal places.)
R6 =
(b) Repeat part (a) with midpoints as the sample points.
M6 =
Express the limit as a definite integral on the given
interval.
lim n → ∞
n
7xi* +
(xi*)2
Δx, [3, 8]
i = 1
8
dx
3

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

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