Homework Problems 1.pdf - 1 a)\u200b \u200bThe Intermediate Value Theorem states that if f(x is a continuous function on the interval[a,b and d

# Homework Problems 1.pdf - 1 a)u200b u200bThe Intermediate...

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1.a)The Intermediate Value Theorem states that if f(x) is a continuous function on the interval [a,b] and d [f(a),f(b)], then there is a c [a,b] such that f(c)= d. b)The Mean Value Theorem states that if f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b) then there is at least one number c in the interval (a,b) such that f’(c} = f(b)-f(a)/(b-a). c)Rolle’s Theorem states that when f(a)=f(b), we have f’(c)=0. Then there exists a point in the interval (a,b), c where f’(c)=0. d)The Mean Value Theorem for Integrals states that if f is a continuous function on the closed interval [a,b] then there is at least one number c, a≤c≤b, so that f(c)(b-a)=. e)The Weighted Mean Value Theorem for Integrals states that if f(x) and g(x) is continuous on [a,b] and g(x) is positive for any x [a,b], then there exists a c (a,b) such that . 2.Code on the next page. 3.Solving for , we get .85914. For h=1/10, taking |.85914- 0.865089832179|, the error is 0.0059. For h=1/20, taking |.85914- 0.860630663406|, the error is 0.001491.