For f, g,h and h(i) Consider the function f: RR defined byf(x) = 12x³.By using definition, explain whether f is differentiable on R. Deducethe continuity of f on R.(a)(b)(c)(d)(e)(f)(g)(h)(i)1f'Let f' be the first derivative of f computed in (a). Is is Riemannintegrable on [-1, 1]? Explain.Evaluatewith the partitionS1f'(x)Pn = {1, fill in, the blankde by using the definition of Riemann integralHint: (1) Each (sub)interval is given by(2) Use the formulaei=1[fill in, the blank], 1≤i≤n.1(n+i-1)2,2}, ne N.12n37+8n² 48n³+0n51137=(n+ 5)² - 2 + 80² + 45m² +0 (-1).2n8n2 48n³i=1Determine the range f(A) where A = (a, 0] for some fixed a < 0,a #Determine the supremum sup(f(A)\{0}), if exists.Is f(A) open in R? Explain.Is f(A) connected? Explain.Is f(A) compact? Explain.xnFor each n E N, consider n =Define the sequence {9n} by 9n (x):= f(xn),of {9} if exists.with x R+ = {x ER | x>0}.ER+. Find the limit function

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Answered: Is f(A) open in R? Explain. Is f(A)…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Is f(A) open in R? Explain. Is f(A) connected? Explain. Is f(A) compact? Explain. x For each nN, consider n = Define the sequence {gn} by gn(x):= f(n), n of {9} if exists. with a R+ = {x ER | x>0}. ER+. Find the limit function.