L00 0.75 The error function is defined by 0.50 0.25 2 erf(z) = Co.00 1. dt %3D -0.25 -0.50 for all values of x. -0.75 -1.00 There is no antiderivative of e-² formed from polynomial, root, exponential, logarithmic, trigonometric functions. Yet the crror function has significant uses in probability, statistics, and other ficlds; so computing accurate estimates is important. which is an elementary function, ie. one which can be (a) Use a Riemann sum with 4 subintervals to estimate the value erf(0.2). (b) By replacing e¯² with its degree four Taylor polynomial about a = 0 (which can be integrated), find another estimate for the value of erf(0.2). (c) Repeat parts (a) and (b) for the value erf(2) (d) Provide sketches for parts (a)-(c). For example, sketch Ricmann sums and regions bencath appropriate curves. (c) Are accurate cstimates obtained in parts (a)-(c)? Why or why not? What changes would result in more accurate estimates? (x)j10
L00 0.75 The error function is defined by 0.50 0.25 2 erf(z) = Co.00 1. dt %3D -0.25 -0.50 for all values of x. -0.75 -1.00 There is no antiderivative of e-² formed from polynomial, root, exponential, logarithmic, trigonometric functions. Yet the crror function has significant uses in probability, statistics, and other ficlds; so computing accurate estimates is important. which is an elementary function, ie. one which can be (a) Use a Riemann sum with 4 subintervals to estimate the value erf(0.2). (b) By replacing e¯² with its degree four Taylor polynomial about a = 0 (which can be integrated), find another estimate for the value of erf(0.2). (c) Repeat parts (a) and (b) for the value erf(2) (d) Provide sketches for parts (a)-(c). For example, sketch Ricmann sums and regions bencath appropriate curves. (c) Are accurate cstimates obtained in parts (a)-(c)? Why or why not? What changes would result in more accurate estimates? (x)j10
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 51RE
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
Transcribed Image Text:L00
0.75
The error function is defined by
0.50
0.25
2
erf(z) =
Co.00
1.
dt
%3D
-0.25
-0.50
for all values of x.
-0.75
-1.00
There is no antiderivative of e-²
formed from polynomial, root, exponential, logarithmic, trigonometric functions. Yet the
crror function has significant uses in probability, statistics, and other ficlds; so computing
accurate estimates is important.
which is an elementary function, ie. one which can be
(a) Use a Riemann sum with 4 subintervals to estimate the value erf(0.2).
(b) By replacing e¯² with its degree four Taylor polynomial about a = 0 (which can be
integrated), find another estimate for the value of erf(0.2).
(c) Repeat parts (a) and (b) for the value erf(2)
(d) Provide sketches for parts (a)-(c). For example, sketch Ricmann sums and regions
bencath appropriate curves.
(c) Are accurate cstimates obtained in parts (a)-(c)? Why or why not? What changes
would result in more accurate estimates?
(x)j10
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