1. Consider the error function, erf(x), defined by erf(x) = e-* dt. This function is important in probability and statistics. (a) Sketch the graph y = e=x². (b) Determine the intervals of decrease and/or increase of erf(x). (Hint: what is the derivative of erf(x)?) d (c) Find erf(/). [Hint: Apply the second Fundamental Theorem of Calculus (FTC) da and the chain rule.]
1. Consider the error function, erf(x), defined by erf(x) = e-* dt. This function is important in probability and statistics. (a) Sketch the graph y = e=x². (b) Determine the intervals of decrease and/or increase of erf(x). (Hint: what is the derivative of erf(x)?) d (c) Find erf(/). [Hint: Apply the second Fundamental Theorem of Calculus (FTC) da and the chain rule.]
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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![1. Consider the error function, erf(x), defined by
erf(z) = .
´dt.
e
This function is important in probability and statistics.
(a) Sketch the graph y = e=x².
(b) Determine the intervals of decrease and/or increase of erf(r). (Hint: what is the
derivative of erf(r)?)
(c) Find erf(VT). [Hint: Apply the second Fundamental Theorem of Calculus (FTC)
dx
and the chain rule.]
2. In this problem we will see how to use Riemann Sums to calculate In(2).
(a) According to the Fundamental Theorem of Calculus which bound b is needed to get
| Edr = In(2)? Show your work.
(b) Draw the rectangular figure corresponding to a left endpoint Riemann sum with n = 5
rectangles with equal bases. Is this an over or an under estimate?
y = =
1
2
(c) Give a clear explanation of how to estimate/calculate In(2) to within an accuracy of ɛ,
for example, e = 0.01. Specifically how many subdivisions are needed?
(d) With n = 5 compare the left endpoint approximation L5, the right endpoint
approximation R5 and their average to In(2) (use a calculator.) Which is best?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe06db80f-7881-47d0-9ae3-5e056ca14fa2%2F7e89c3fc-3a5a-4fe7-95ae-8d67cd5fb505%2Fh3d92ln_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the error function, erf(x), defined by
erf(z) = .
´dt.
e
This function is important in probability and statistics.
(a) Sketch the graph y = e=x².
(b) Determine the intervals of decrease and/or increase of erf(r). (Hint: what is the
derivative of erf(r)?)
(c) Find erf(VT). [Hint: Apply the second Fundamental Theorem of Calculus (FTC)
dx
and the chain rule.]
2. In this problem we will see how to use Riemann Sums to calculate In(2).
(a) According to the Fundamental Theorem of Calculus which bound b is needed to get
| Edr = In(2)? Show your work.
(b) Draw the rectangular figure corresponding to a left endpoint Riemann sum with n = 5
rectangles with equal bases. Is this an over or an under estimate?
y = =
1
2
(c) Give a clear explanation of how to estimate/calculate In(2) to within an accuracy of ɛ,
for example, e = 0.01. Specifically how many subdivisions are needed?
(d) With n = 5 compare the left endpoint approximation L5, the right endpoint
approximation R5 and their average to In(2) (use a calculator.) Which is best?
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