Using the results above and the Intermediate Value Theorem we conclude that there is a solution to the equation:

Question

1)

a=0

b-pi

Using the results above and the Intermediate Value Theorem we conclude that there is a solution to the equation:

cos(2x)=4-3x for some c E:

2)

a=0

b-1

Using the results above and the Intermediate Value Theorem we conclude that there is a solution to the equation:

sqrt(x) +2x=2 for some c E:

3)

a=3

b-6

Using the results above and the Intermediate Value Theorem we conclude that there is a solution to the equation:

(1/(x-2))+(1/(x-9))=0 for some c E:

Answer 1

Let f(x) = cos(2x) + 3x - 4

f is continuous on the interval [0, π]

f(0) < 0 and f(π) > 0

So, by the IVT, f(c) = 0 for some number c between 0 and π

cos(2c) + 3c - 4 = 0

So, cos(2c) = 4 - 3c

Do the other problems in a similar manner.