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Educational Level
Secondary school, High school and College
Program Purpose
Provide step by step solutions of your problems using online calculators (online solvers)
Problem Source
Your textbook, etc

2.
Numerical Differentiation
Numerical Differentiation using Newton's Forward, Backward Method
1. From the following table of values of x and y, obtain `(dy)/(dx)` and `(d^2y)/(dx^2)` for x = 1.2 .
x
1.0
1.2
1.4
1.6
1.8
2.0
2.2
y
2.7183
3.3201
4.0552
4.9530
6.0496
7.3891
9.0250

2. From the following table of values of x and y, obtain `(dy)/(dx)` and `(d^2y)/(dx^2)` for x = 2.2 .
x
1.0
1.2
1.4
1.6
1.8
2.0
2.2
y
2.7183
3.3201
4.0552
4.9530
6.0496
7.3891
9.0250

3.
Numerical Integration
Numerical Integration using Trapezoidal, Simpson 1/3, Simpson
3/8 Rule
1. From the following table, find the area bounded by the curve and x axis from
x=7.47 to x=7.52 using trapezodial, simplson 1/3, simplson 3/8 rule.
x
7.47
7.48
7.49
7.50
7.51
7.52
f(x)
1.93
1.95
1.98
2.01
2.03
2.06

2. Evaluate I = `int_0^1 (1)/(1+x) dx` by using simpson's rule with h=0.25 and h=0.5

5. Solve numerical differential equation using Euler, Runge-kutta 2, Runge-kutta 3, Runge-kutta 4 methods
1. Find y(0.1) for `y'=x-y^2`, y(0) = 1, with step length 0.1
2. Find y(0.5) for `y'=-2x-y`, y(0) = -1, with step length 0.1
3. Find y(2) for `y'=(x-y)/2`, y(0) = 1, with step length 0.2
4. Find y(0.3) for `y'=-(x*y^2+y)`, y(0) = 1, with step length 0.1
5. Find y(0.2) for `y'=-y`, y(0) = 1, with step length 0.1

4.
Numerical Interpolation
Numerical Interpolation using Forward, Backward Method
1. The population of a town in decimal census was as given below. Estimate population for the year 1895.
Year
1891
1901
1911
1921
1931
Population
(in Thousand)
46
66
81
93
101

2. Let y(0) = 1, y(1) = 0, y(2) = 1 and y(3) = 10. Find y(4) using newtons's forward difference formula.
3. In the table below the values of y are consecutive terms of a series of which the number 21.6 is the 6th term. Find the 1st and 10th terms of the series.
X
3
4
5
6
7
8
9
Y
2.7
6.4
12.5
21.6
34.3
51.2
72.9

4. The population of a town in decimal census was as given below. Estimate population for the year 1895.
X
0.10
0.15
0.20
0.25
0.30
tan(X)
0.1003
0.1511
0.2027
0.2553
0.3073

Find (1) tan 0.12 (2) tan 0.26
5. Certain values of x and log10x are (300,2.4771), (304,2.4829), (305,2.4843) and (307,2.4871). Find log10 301.
6. Find lagrange's Inerpolating polynomial of degree 2 approximating the function y = ln x defined by the following table of values. Hence find ln 2.7
X
2
2.5
3
ln(X)
0.69315
0.91629
1.09861

7. Using the following table find f(x) as polynomial in x
x
-1
0
3
6
7
f(x)
3
-6
39
822
1611