Answer only the parts written in blue in the images below Mathematics can smile!3PROBLEM Two(a) Using Newton's forward difference formula, find the sumS, = 1³ +2³ +3³ +4³ + ... +n³.(b) Values of x (in degrees) ans sinx are given in the following table.x (in degrees)sinx150.25881900.34202010.42261832025300.50.57357640.64278763540Determine the value of sin 38º.(c) Find the missing term in the following table:y1129381Explain why the result differs from 3³ = 27.(d) From the following table, find the value of el.17 using Gauss's forward formula.et1.00 2.7183| 1.05 | 2.85771.10 3.00421.15 | 3.15821.20 3.32011.25 3.49031.30 | 3.6693(e) The following table gives the values of e for certain equidistant values of x. Find the valueof e when x= 0.644 by using:(i) Bessel's Formula(ii) Stirling's Formula.(iii) Everett's formula.(f) Derive the Lagrange Interpolation formula.(g) The following table gives the values of the probability integral2y =Mathematics can smile!corresponding to certain values of x.For what value of x is this integral equal to ?0.460.470.480.49y 0.4846555 | 0.4937452 | 0.5027498 | 0.5116683(h) The values of f(x) are given at a,b,c.Show that the maximum is obtained byf(a).(b² – c²) + f(b).(c² – a²) + f(c).(a² – b²)2[f(a).(b – c)+f(b).(c– a)+f(c).(a – b)](i) Given log10654=2.8156, log10658 =2.8182,log10659 =2.8189,log10661 =2.8202, find log1065(j) Derive the general error formula. PROBLEM FOUR(a) Find the value of x when y =0.3 by applying Lagrange's formula inversely.x 0.4y| 0.3683| 0.3332 | 0.28970.60.8(b) The following table gives the value of the elliptical integralF(0) =1- įsin²0for certain values of 0.Find the values of 0 if F(0)=0.3887250230F(0) 0.3706 0.4068| 0.4433210(c) Use Lagrange multipliers to obtain the interpolating polynomial which passes throuthe following points.-11 2f(x) | 0Hence use your polynomial to approximate f'(x), f"(x), f" (x), f'(1), f"(1), f" (1).(d) Using Lagrange's formula, find a polynomial which passes through the points-10 15(0, – 12), (1,0), (3,6), (4, 12)Mathematics can smile!6(e) Using Lagrange's interpolation formula, find the value of y corresponding to x= 10the following table:511y= f(x) | 121314 16(f) Given that u =F, ɛr, ɛy and & denote the errors in x,y and z respectively sucix= y=z=1 and ɛ = ɛ, = & = 0.001, then find the relative maximum error in u(g) Show that the relative error in quotient of two quantities x and y may be expresdifference between the relative errors in x and y.Sxy?(h) Given that u = , &, &, and ɛ denote the errors in x,y and z respectively sucx=y=z=2 and & = ɛy = & = 0.003, then find the relative maximum error in u(i) The number x= 37.46235 is rounded off to 4 significant figures.Compute the percentage error in x.(j) Obtain an interpolating polynomial using Newton Backward Difference Formula for-12f(x)0 -1 | 0| 15PROBLEM FIVE(a) Derive the trapezoidal Rule and the error involved in this method Hence or otheevaluate:(i)(b) Use Romberg integration to compute1-Ldx1+xcorrect to three decimal places.(c) erive the Simpson's third Rule and the error involved in this method Hence or otheevaluate:(i)(d) In the following table, locate and correct the value of y that is in error by using difftable, in which y is a cubic polynomial in x.x|01 2y 25 | 21 | 18 | 184 545 76 | 1233727(e) Use Romberg's method to computedxcorrect to 4 decimal places by taking h=0.5,0.25 and 0.125.(f) Given that1.01.21.41.61.82.02.2

a Given that Sn=13+23+33+...+n3 By using 1-x-2=1+2x+3x2+4x3+.....+n+1xn By multiplying x in…

(a) Using Newton's forward difference formula, find the sum Sn = 13 +2° +3³ +4³ +. +n°. (b) Values of x (in degrees) ans sinx are given in the following table. x (in degrees) sinx 15 | 0.2588190 0.2420001

(a) Using Newton's forward difference formula, find the sum Sn = 13 +2° +3³ +4³ +. +n°. (b) Values of x (in degrees) ans sinx are given in the following table. x (in degrees) sinx 15 | 0.2588190 0.2420001

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Find Jul, Ivl, 12ul, , lu + vl, lu- vl, and Jul - Ivl. i+ 4j, =i-2j Ju + v = %3D Ju-vl = %3D lul -…

Q: Question 8 The team installing the conveyor belts has a measuring tape in imperial units. Determine…

A: To convert the given length in feet.

Q: Draw the missing information in the triangle

A: Given: Draw the missing information in the triangle

Q: An angle has measurement 98.6 degrees. What would be the measurement, in degrees, of a supplementary…

Q: In acute triangle ABC, side b= 12, side c = 10 and mLA = 42. Find side a. %3D

A: We will use cosine law to answer this

Q: 2x + 2 7x + 11 4x-28

Q: Kansas City, MO and St. Louis, MO are 248 miles apart. On a map, these two cities are 4.9…

A: Kansas City, MO and St. Louis, MO are 248 miles apart. On a map, these two cities are 4.9 cm apart.…

Q: if a= 9 and A=85 degrees, what is b, c, & B?

Q: Find the measure of 0 in the triangle. Do not use a calculator. 2/2+5 B C. B = 2. 2.

A: Apply the cosine rule, cosB=a2+c2-b22acorcosB=AB2+BC2-AC22(AB)(BC)

Q: Step 3: Fill out the following chart. Make sure you pay attention to the unit use kilometers and…

Q: The Sierpinski triangle is a fractal created from an equilateral triangle. At each stage, the…

A: This question can be solved suing the concept of geometric progression.

Q: Interpreting numbers in advertising or product descriptions can be problematic. Data can be…

Question

100%

Answer only the parts written in blue in the images below

Mathematics can smile!
3
PROBLEM Two
(a) Using Newton's forward difference formula, find the sum
S, = 1³ +2³ +3³ +4³ + ... +n³.
(b) Values of x (in degrees) ans sinx are given in the following table.
x (in degrees)
sinx
15
0.2588190
0.3420201
0.4226183
20
25
30
0.5
0.5735764
0.6427876
35
40
Determine the value of sin 38º.
(c) Find the missing term in the following table:
y
1
1
2
9
3
81
Explain why the result differs from 3³ = 27.
(d) From the following table, find the value of el.17 using Gauss's forward formula.
et
1.00 2.7183
| 1.05 | 2.8577
1.10 3.0042
1.15 | 3.1582
1.20 3.3201
1.25 3.4903
1.30 | 3.6693
(e) The following table gives the values of e for certain equidistant values of x. Find the value
of e when x= 0.644 by using:
(i) Bessel's Formula
(ii) Stirling's Formula.
(iii) Everett's formula.
(f) Derive the Lagrange Interpolation formula.
(g) The following table gives the values of the probability integral
2
y =
Mathematics can smile!
corresponding to certain values of x.For what value of x is this integral equal to ?
0.46
0.47
0.48
0.49
y 0.4846555 | 0.4937452 | 0.5027498 | 0.5116683
(h) The values of f(x) are given at a,b,c.Show that the maximum is obtained by
f(a).(b² – c²) + f(b).(c² – a²) + f(c).(a² – b²)
2[f(a).(b – c)+f(b).(c– a)+f(c).(a – b)]
(i) Given log10654=2.8156, log10658 =2.8182,log10659 =2.8189,log10661 =2.8202, find log1065
(j) Derive the general error formula.

PROBLEM FOUR
(a) Find the value of x when y =0.3 by applying Lagrange's formula inversely.
x 0.4
y| 0.3683| 0.3332 | 0.2897
0.6
0.8
(b) The following table gives the value of the elliptical integral
F(0) =
1- įsin²0
for certain values of 0.Find the values of 0 if F(0)=0.3887
250
230
F(0) 0.3706 0.4068| 0.4433
210
(c) Use Lagrange multipliers to obtain the interpolating polynomial which passes throu
the following points.
-1
1 2
f(x) | 0
Hence use your polynomial to approximate f'(x), f"(x), f" (x), f'(1), f"(1), f" (1).
(d) Using Lagrange's formula, find a polynomial which passes through the points
-10 15
(0, – 12), (1,0), (3,6), (4, 12)
Mathematics can smile!
6
(e) Using Lagrange's interpolation formula, find the value of y corresponding to x= 10
the following table:
5
11
y= f(x) | 12
13
14 16
(f) Given that u =
F, ɛr, ɛy and & denote the errors in x,y and z respectively suci
x= y=z=1 and ɛ = ɛ, = & = 0.001, then find the relative maximum error in u
(g) Show that the relative error in quotient of two quantities x and y may be expres
difference between the relative errors in x and y.
Sxy?
(h) Given that u = , &, &, and ɛ denote the errors in x,y and z respectively suc
x=y=z=2 and & = ɛy = & = 0.003, then find the relative maximum error in u
(i) The number x= 37.46235 is rounded off to 4 significant figures.
Compute the percentage error in x.
(j) Obtain an interpolating polynomial using Newton Backward Difference Formula for
-1
2
f(x)
0 -1 | 0| 15
PROBLEM FIVE
(a) Derive the trapezoidal Rule and the error involved in this method Hence or othe
evaluate:
(i)
(b) Use Romberg integration to compute
1-L
dx
1+x
correct to three decimal places.
(c) erive the Simpson's third Rule and the error involved in this method Hence or othe
evaluate:
(i)
(d) In the following table, locate and correct the value of y that is in error by using diff
table, in which y is a cubic polynomial in x.
x|01 2
y 25 | 21 | 18 | 18
4 5
45 76 | 123
3
7
27
(e) Use Romberg's method to compute
dx
correct to 4 decimal places by taking h=0.5,0.25 and 0.125.
(f) Given that
1.0
1.2
1.4
1.6
1.8
2.0
2.2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Trending now

This is a popular solution!

Step by step

Solved in 6 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Finite State Machine$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Create a question for the following image then describe the steps to solve for the area of the shaded space
What are the values of A and B? A A = [ ? ]° 2/3 4 B = 2]
Find the exact values of the side lengths h and a
A. Determine the percentage of a circle's circumference cut off by an angle that has a measure of 65.7 degrees plus 0.6 radians. B. degrees radians
Shade each set region: Identify elements that would be included in these regions based on the Figure 1. (AU B) nC
TASK 1: Area and Perimeter Use the five pentominoes cutout shapes on the next page to answer the questions below. NOTE: The side length of each square that makes up the pentominoes is 1-unit, the perimeter of the square is 4 units and the area of the square is one square unit. a. Find the area and perimeter of each of the five selected pentominoes below. What patterns do you notice? b. Using all of the five shapes below, put the pieces together to create the shape with the smallest perimeter. C. Using all of the five shapes below, put the pieces together to create the shape with the largest perimeter. d. Of ALL of the pentominoes (12 total) which has the largest perimeter and which has the smallest perimeter? Draw the shapes that you created. Carefully explain your answers to show your conceptual understanding of the content by providing a justification for someone that might not understand the problem. Provide a strong, detailed explanation with enough detail, use of precise…
CHAPTER 5. EUCLIDEAN TRIANGLES 144 %3D CE = 10 feet, and EB = 12 feet. Find DB. D B
David counted the number of take-out meals sold at a restaurant during a week. He drew the pictograph below, with each fork representing 10 meals. Monday Tuesday Wednesday = 10 meals Thursday Friday Saturday Sunday How many meals were sold on Tuesday?