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: →0 (2a−3/2a+ 5)^(2a+1) should i use lhopital or direct substitute the value of

A:

Q: f(x) = -9 f'(x) = -(x²+9) (x²-9)2 f"(x) = 2x(x²+27) (x²–9)3 4. Given a) Provide a complete analysis…

A: a)

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: Use synthetic division to find 1"(-1) and f"(-1) where f(x)= 3x'-8x + 5x-2x' + 5x +13

A: To find the f'''-1 and f4-1 Given that the  fx=3x7-8x6+5x4-2x3+5x+13 f'x=21x6-48x5+20x3-6x2+5…

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: 2 f(x) = √4-x² [-1,1] n = 4 a = -1 right left & middle hand rule b=

A: The given function is fx=4-x2 over the interval -1, 1. The number of subintervals is n=4.

Q: What is the x=g(x) that will diverge the root of f(x) = x3 + 4x2 - 10?

A:

Q: csc/x+5 xp- 1) Use substitution method to evaluate Vx+5

A: Given:         ∫csc2x+5x+5dx     apply u-substitution     u=x+5→dudx=12x+5       dx=2x+5du…

Q: lef f(x) = x-2₁ g(x) = ³√x₁ h(x)=x4, and j(x) = 4x, Express oach of the function. given below one or…

A:

Q: Show that the product rule works for the case f (x) = x2, g (x) = x3.

A: Given that, fx=x2gx=x3 We have to show that the product rule works for the case of given functions.

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: Find the zeros of the polynomials f (x)=x'-5x² – 2x + 24, If it is given that the product of its two…

A: *to find:- roots of the given equation.

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.