Midterm_Soln.pdf - Math 104A Midterm Name Perm Directions You must show all your work to receive full credit If you need extra room you may use the back

Midterm_Soln.pdf - Math 104A Midterm Name Perm Directions...

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Math 104A - Midterm Name: Perm#: Directions : You must show all your work to receive full credit . If you need ex- tra room, you may use the back of the page, but clearly mark which problem you are solving. 1(a)5 ptsState the intermediate value theorem.IffC[a, b], then for everyKbetweenf(a) andf(b), there is somec[a, b]such thatf(c) =K.1(b)5 ptsUse the intermediate value theorem to show thatx5-x4+x3-x2+x-2 = 0has at least one solution. 5 ptsUsing your results from part (b), perform two iterations of the bisectionmethod. 5 ptsHow many iterations of the bisection method would be required to guaranteean approximation that is within 10-4of the true solution?

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