Solutions Homework 4 - MATH 106 CALCULUS I FOR BIO SOC SCI FALL 2011 INSTRUCTOR JOSE MANUEL GOMEZ Solutions Homework 4 Please show all your work(1(5

Solutions Homework 4 - MATH 106 CALCULUS I FOR BIO SOC SCI...

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MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011 INSTRUCTOR: JOS ´ E MANUEL G ´ OMEZ Solutions Homework 4. Please show all your work. (1) (5 Points) Use the intermediate value theorem to show that there exists somexinthe interval [0,π2] for whichcos(x) =2xπ. (2) (5 Points) Show that the polynomialp(x) =x4x210x+ 1 has at least one root.(Recall that a root of a polynomialp(x) is a numbercfor whichp(c) = 0.)

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