Calculus Answers

Find the domain of the function f, defined by f(x)=√(x^3{9-x})

Find the indicated limit, if it exists.

limit of f of x as x approaches negative 1 where f of x equals 4 minus x when x is less than negative 1, 5 when x equals negative 1, and x plus 6 when x is greater than negative 1

Write an odd natural number as a sum of two integers m1 and m2 in a way that m1m2 is maximum.

∫_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)