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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
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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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)
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,

y=ln(t+1) and y=t on [0,∞)

Let Ax denote the area beneath y=lnt+1 and let Bx denote the area beneath y=t, both over [0,x].

Then,

Ax=∫0xln(t+1)dt=xln(x+1)+ln(x+1)-x

B(x)=∫0xtdt=23x32

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