Provide an appropriate response.Use the Intermediate Value Theorem to prove that 9x3 + 3x2 - 9x - 8 = 0 has a solution between 1 and 2.
What will be an ideal response?
Let f(x) = 9x3 + 3x2 - 9x - 8 and let y0 = 0. f(1) = -5 and f(2) = 58. Since f is continuous on 
and since y0 = 0 is between f(1) and f(2), by the Intermediate Value Theorem, there exists a c in the interval (1 , 2) with the property that f(c) = 0. Such a c is a solution to the equation 
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Find an equation for the ellipse described.Center at (0, 0); focus at (0, 4); vertex at (0, -7)
A. 
+ 
= 1
B. 
+ 
= 1
C. 
+ 
= 1
D. 
+ 
= 1
Provide an appropriate response.What conditions, when present, are sufficient to conclude that a function f(x) is continuous at 
A. f(a) exists, the limit of 
as 
from the left exists, and the limit of 
as 
from the right exists.
B. f(a) exists, the limit of 
as 
exists, and the limit of 
as 
is 
C. f(a) exists, and the limit of 
as 
exists.
D. The limit of 
as 
from the left exists, the limit of 
as 
from the right exists, and these two limits are the same.
Solve the equation. Express radicals in simplest form.(r + 6)2 = 15
A. -6 + 
, -6 - 
B. 9
C. 6 + 
, 6 - 
D. 
, 
Simplify the expression. Assume that all variables are non-negative.
A. 4
B. 8
C. 4
D. 4