Provide an appropriate response.Plot the functions u(x) = 9, l(x) = 9 - x2, and f(x) = 8 + cos2x. Then use these graphs along with the Squeeze Theorem to prove that f(x) = 9 .

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From the graph, it can be seen that the graph of f(x) = 8 + cos2 x is between the graphs of l(x) = 9 - x2 and u(x) = 9. Also l(x) = 9 and u(x) = 9. Since the graph of f(x) = 8 + cos2x is squeezed between the graphs of  and u(x) = 9, both of which go to 9 as x?0, by the Squeeze Theorem we can conclude that f(x) = 9.

Mathematics

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Find the extreme values of the function subject to the given constraint.  

A. Maximum: 81 at    minimum: 9 at  
B. Maximum: 77 at    minimum: 13 at  
C. Maximum: 49 at    minimum: 41 at  
D. Maximum: 77 at    minimum: 13 at  

Mathematics

Provide an appropriate response.Find the total area.

A. 4x2 + 6x + 9 B. 4x2 + 12x + 9 C. 2x2 + 12x + 9 D. 2x2 + 6x + 9

Mathematics

Tell whether the pair of ratios forms a proportion. Answer yes or no. ? ,

What will be an ideal response?

Mathematics

Solve the compound inequality. Express the solution using interval notation. Graph the solution set.x ? 5 and x ? 4

A. [4, ?)

B. [4, 5]

C. (-?, 4]

D. (-?, 4] ? [5, ?)

Mathematics