CPhill

1. We are trying to find the intervals  where the function is "rising" from left to right

One interval   is (-inf, 0)

Can you find the other one ???

2.  If the function is constant.....it wll be paralel to the y axis (a horizontal line)

This happens on the interval (-4, 0)

sum ≈  1.499999.....    =   1.5

I think this also might be

lim         sin(6x) / [ x + tan(9x) ]

x→0

Using L'Hopital's Rule we have

lim         6cos(6x) /[ 1 + 9sec^2(9x) ]    =     6(1)  / [ 1 + 9 ]  =  6 /10    =  3 / 5

x→0

V_sphere =   (4/3) pi * radius^3 =  (4/3) (3.14) (3)^3 ≈  113 ft^3

I'll finish d and e in a little while....

a. Solve the equation (x+3)(x-3) = x-3 

x^2 - 9 = x - 3

x^2 -x - 6 = 0

(x -3) ( x + 2) = 0

Settting each factor to 0 and solving for x  gives that x = 3  and x = -2

b. These are the x coordinates of the intersections of  both functions

c. g(x) = h(x)

-.5x^2 + x + 3 =  x - 3 

-.5x^2 + 6 = 0

.5x^2 = 6

x^2 = 12

x = ±√12  = ±2√3

Thanks, DBZ

Math Forum....not a Politics Forum....!!!

Function A

f(x)  =  1 / ( x - 3)

The  vertical asymptote is  the value of x that makes x - 3 = 0 ⇒   x = 3

The vertical asymptote of B   is  x = 4

So....

Function A has a vertical asymptote at x = 3.
Function B has a vertical asymptote at x = 4.

Nice, EP  !!!

Diameter = 8.5 cm

So

Radius = 4.25

V_cone =   3.14 * (radius)^2 * height /3  =   3.14 * (4.25)^2 * 4.5  / 3   ≈  85.07 cm^3