Finding the circumference of a circle
Need to know the formula for finding area and circumference of a circle 2
Finding a rule for a sequence.
Find the rule for the sequence below. square 2x2 =10 3x3=40 +30=20 difference 4x4=90+50=20 difference 5x5=160+70=20 difference
Comparing euler's method to improved euler's method
y'= 1/2 - (X)+2x when y(0)=1
Find the exact solution of ___ O/ <
Euler's and improved Euler's method,...find the exact solution
1. y'=1/2 -x + 2y y(0) = 1 Find the exact solution "Sphee" {0 with line diagonal of the 0} 2. y'=x square + y square y(0)=1 a. Let h=.1 use Euler and improve to approximate to get Sphee(.1 ...continues
Prove using Euler method
Solve a polynomial (search the roots and factorize it) using the method of substitution.
Given the polynomial obtain the roots of it.
Show that there are exactly two solutions of the following equation, and find them
Show that there are exactly two solutions of the following equation, and find them (where ln(x) is the natural logarithm function) ln(2x squared - 1) - 2ln(2 + x) = 0
Working with iterative methods.
The sequence of value given by the iterative formula is X n+1=2/9-lnXn with initial value X=1,converges to alpha. 1) State an equation satisfied by alpha, and hence show that alpha is the x coordinate of a point on the curve where y=3. 2) Use this iterative formula to find alpha correct to 2 decimal places, showin ...continues
Given The Maclaurin series for the inverse hyperbolic tangent is of the form x+x^3/3+x^5/5...x^7/7. Show that this is true through the third derivative term.
Differentiation of Polynomials : Proofs
Please see the attached file for the fully formatted problems. Let g be a function which can be differentiated four times on the interval [-1,1]. Denote . 1) Show that when g is a polynomial of degree less than or equal to 3. 2) Let P be the interpolation polynomial of f at the points -1, , , 1. a) Show that . b ...continues
