12n+1) x Pa (x) : (n +1) Prte tx) +n Pane (x) a) Get the Le gendre reconnection polynomials using the; P(x, 2)= (1-2x2 +2?)2_ Pn(x)g^ generodór function of b) Show that; m tn for S Pm (x) Pn (x)dx -Q -1 Note; Legendre equation; (1-x²) pm lx) - 2xPm(x) + mlmel) Pm (x) 0

Q: 4 find the difference quoitent of... f(x) = -√x-19

A: To find the difference quotient of the following function.fx=x-19

Q: USE +¹ (f(x)) =X a] if yinv b] the value of the value of d] f (3) if 3 = f¹ (2) 1 √x-7 to inv…

A:

Q: Suppose that f(x)=(x+2)(x-2)^2. (G) Use interval notation to indicate where f(x) is concave down.…

A:

Q: let F(x)=f(f(x)) and G(x)=(F(x))^2  You also know that f(5)=10 , f(10)=3,  f prime of 10 = 4, f…

A: The objective of the question is to find the derivative of the functions F(x) and G(x) at x = 5. We…

Q: A power function has the form: f(x) = c x x^k where c is any real number and k is an integer.…

A:

Q: Let f(x) = e^x. Find the polynomial P2(x) of degree at most 2 such that P2(1) = f(1), P2(2) = f(2),…

A: We have to find the polynomial of degree 2 for the function fx=ex using the divided difference…

Q: given that f(x) =x-1, and g(x) =2x2 -1, determine (g (dot product) f)(x)     i put "(dot…

A: The given function is: f(x)=x-1           and             g(x)=2x2-1

Q: Lat f(2) -- nr +5 and g(2) - ma +2-1. The functiors are combined to form a new function h(z) - S(2)…

A:

Q: Consider the Lagrange polynomial that passes through the 4 data points given by 2 8 y 7 | 151 | 407…

A: We know that L0x is given by  L0x=x-x1x-x2x-x3x0-x1x0-x2x0-x3        1 Here, x0=2,x1=5,x2=7,x3=8,x=4…

Q: Given the function h (x) = 9x¹ - x² A) Factor: h(x)= [Select] B) Determine the real zeros: [Select]…

A:

Q: 8x-7 4. Let f)7x + 10 (a) Find f (x). (b) Find thedomain of/. (c) Find the domain of f (d) Find the…

A: (a) Find the inverse of f (x).

Q: Let f(x) = x3 + 5. Explain why f(x) is invertible, then show all steps in the derivation of a…

A: Invertible function and it's inverse.

Q: Find the following using the rule indicated (only): i) If f(x) = (6x? – 8) (3x + 2), find f'(3)…

A:

Q: (b) (2 points) use the Concavity Theorem to determine where f(x) is concave up and where it is…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.