M408C - HW 4 - 1 1b Form the function f x = x 2 x − 1 on...

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P ROBLEMS H W 4 3.3 P AGE 144 1, 5, 9, 15, 23, 27, 29, 41 (repeat) 3.4 P AGE 154 3, 11, 15, 17, 19, 31, 35 (repeat) 3.5 P AGE 161 1, 5, 7, 11, 21, 25, 27, 33, 47 Q UIZ 3 You will need a calculator for this quiz Instead of online sample propblems, do the problems from the book: Some good problems to study: Page 105, Problems 45, 47, 48, but change the problems as follows. Find an interval (a,b) for each equa- tion where f(a), f(b) change sign. Find the secant line, as we did in class, through (a, f(a)) and (b, f(b)). Find the point c where the secant line intersects the x-axis. Use that as a guess for the solution to the equation. How close a guess is it? That is, compute f(c) and see how close to zero it is. Quiz 3c 20 min 1a) Use the Intermediate Value Theorem to show that the equation x 2 + x = 1 has a solution in the interval [0
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Unformatted text preview: , 1]. 1b) Form the function f ( x ) = x 2 + x − 1 on the interval [0 , 1]. Find the equation for the secant line over the interval. 1c) Find where the above secant line intersects the x-axis. The solution you get using the quadratic formula is − 1+ √ 5 2 . How does your solution compare? Quiz 3b 20 min 1a) Use the Intermediate Value Theorem to show that the equation cosx = 1 2 has a solution in the interval [0 , π 2 ]. 1b) Form the function f ( x ) = cos x − 1 2 on the interval [0 , π 2 ]. Find the secant line over the interval. 1c) Find where the above secant line intersects the x-axis, and use that as an estimate of the solution to 1a). The true solution is 60 o or π 3 . How does this compare to the secant solution?...
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This note was uploaded on 03/22/2008 for the course M 408c taught by Professor Mcadam during the Fall '06 term at University of Texas.

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