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Calculus Answers

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∫_0^1▒〖((3x^2-x^2+2x-4))/√(x²-3x+2) dx〗
A piece of wire 14 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.

(a) How much wire should be used for the square in order to maximize the total area?



(b) How much wire should be used for the square in order to minimize the total area?

The position of an object moving along a line is given by the function s(t) = 6t^2 + 36 t. Find the average velocity of the object over the following intervals.

​(a)​ [1, 7​]
​(b) ​[1, 6​]
​(c)​ [1, 5​]
​(d) ​[1, 1plus​h] where h > 0 is any real number.
A force F= 3 i — 6 k acts along a line
passing through the point P(0, — 1, 4).
Determine the torque about the point
Q(4, 6, — 1).
Show that V . (V x F)=0 for a vector
field F .
Find the derivative of f(x) = 8x + 4 at x = 9.

0
4
8
9
If^A=ti-sintj, and^B=costi+sintj+k, find d/dt(^A•^B)
Calculate a unit vector normal to the surface
x3 + y3 + 3xyz = 3 at the point (1, 2, - 1).
A rigid body is rotating with an angular speed of
3.0 rad s-1 about an axis OL = 21 -2j + k,
where 0 is the origin. Determine the velocity of
the body at the point P(4, 1, 2).
What is the integral of 3^x e^x?
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