In class we discussed the relationship between the hyperbolic functions and a hyperbola then showed that it is analogou...
1. In class, we examined in detail case "C" of table 3.4 on page 150 of your text. Prove the expressions provided in the table for cases A, B, and D. Specifically, start from the general equation 3.67, and apply at x-L the boundary condition on the second column of Table 3.4 for each of the cases. Then, solve the differential equation and acquire the information on the third and the fourth column. Hint In some cases, you will need...
Please explain the solution and write clearly for nu, ber 25. Thanks. 25. Approximate the following functions f(x) as a linear combination of the first four Legendre polynomials over the interval [-1,1]: Lo(x) = 1, Li(x) = x, L2(x) = x2-1. L3(x) = x3-3x/5. (a) f(x) = X4 (b) f(x) = k (c) f(x) =-1: x < 0, = 1: x 0 Example 8. Approximating e by Legendre Polynomials Let us use the first four Legendre polynomials Lo(x) 1, Li(x)...
Problem 8 In class, we discussed the difference between a pure (or effect-free) function (i.e. one that returns a value, but does not produce an effect) and a mutating function i.e one that changes the value of its parameters). In this exercise, we ask you to demonstrate your understanding o this distinction by implementing the same functionality as both a pure function, and as a mutating function. Both functions take a list of int as a parameter. The pure variant...