Vt on [0, o0) are quite similar in appearance, The graphs defined by y = In(t+ 1) and y = but as we have seen a number of times this semester, appearances can be deceiving! In this %3D problem, you will compare these graphs by investigating the areas that they bound in the limit. Let A(x) denote the area beneath y = In(t +1) over [0, x], and let B(x) denote the area Vt (also over 0, x). Making sure to indicate by name the techniques/theorems beneath y you are using, compute A(x) lim 200 B(x)
Vt on [0, o0) are quite similar in appearance, The graphs defined by y = In(t+ 1) and y = but as we have seen a number of times this semester, appearances can be deceiving! In this %3D problem, you will compare these graphs by investigating the areas that they bound in the limit. Let A(x) denote the area beneath y = In(t +1) over [0, x], and let B(x) denote the area Vt (also over 0, x). Making sure to indicate by name the techniques/theorems beneath y you are using, compute A(x) lim 200 B(x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
Question

Transcribed Image Text:The graphs defined by y = ln(t + 1) and y = vt on [0, ∞) are quite similar in appearance,
but as we have seen a number of times this semester, appearances can be deceiving! In this
problem, you will compare these graphs by investigating the areas that they bound in the limit.
Let A(x) denote the area beneath y = In(t + 1) over |0, x|, and let B(x) denote the area
beneath y = vt (also over 0, x). Making sure to indicate by name the techniques/theorems
you are using, compute
A(x)
lim
x→∞ B(x)
Expert Solution

Step 1
Given the graphs defined by,
Let denote the area beneath and let denote the area beneath , both over
Then,
Step by step
Solved in 2 steps

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