Please just find the value of limit part B only Definition: The AREA A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectanglesA = lim Rn = lim [f(x1)Aæ + f(x2)Ax+.+f(xn)Aæ]n00n00(a) Use the above definition to determine which of the following expressions represents the area under the graph of f(x) = x° from x = 0 to x = 2.64A. limn00 ni=164В. limii=11С. limn-00 n664D. limnoo n6(b) Evaluate the limit that is the correct answer to part (a). You may find the following formula helpful:n2(n + 1) (2n² + 2n – 1).15 + 25 + 35+...+n³ =12Value of limit =

Answered: Image /qna-images/answer/a5e5ff32-92b7-4f22-b89c-d9b91f1f1615.jpg

Answered: (b) Evaluate the limit that is the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.2: Trigonometric Equations

Problem 96E

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Definition: The AREA A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles.
Definition: The AREA A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles PS: For (a) it is only choosing one of the right selection to determine.
Definition of infinite limit: Let X⊆ R, f: X -> R and a∈ X'. If for every M>0 there exists delta > 0 such that |f(x)| > M whenever x∈X and 0< |x-a| < delta then we say that the limit as x approaches a of f(x) is ∞ which is denoted as lim {x-> a} f(x) = ∞. Suppose a∈R, ∈>0, and f,g : N*(a,∈) ->R. If lim {x-> a} f(x) = L>0 and lim {x-> a} g(x)= ∞, prove lim {x-> a} (fg)(x)=∞.
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Using rectangles each of whose height is given by the value of the function at the midpoint of the rectangle’s base (the midpoint rule), estimate the area under the graphs of the following functions, using first two and then four rectangles. 5. ƒ(x) = x2 between x = 0 and x = 1. 6. ƒ(x) = x3 between x = 0 and x = 1. 7. ƒ(x) = 1/x between x = 1 and x = 5. 8. ƒ(x) = 4 - x2 between x = -2 and x = 2.
1) Let f be the function defined by f(x) = 2^x and let g be defined by g(x) = 4rootx . The region R in the first quadrant is bounded by the graphs of f and g a) find the area of R. b) The region R is the base of a solid whose cross sections are squares perpendicular to the x-axis. Find the volume of this solid. c) The region R is revolves around the line x=4 to generate a solid. Find the volume of this solid.

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(b) Evaluate the limit that is the correct answer to part (a). You may find the following formula helpful: n2(n + 1)2(2n² + 2n – 1) 15 + 25 + 35+. +n° = 25 12 i=1