7. The famous Rodrigues formula states that H, (x) = (-1)"e*² (4)" functions for positive integers for n. What are the functions {H,(x), H,(x), H2(x), H3(x), H4(x)} e-x, where Hn (x) is a sequence of

Q: The average classroom teacher's salary is given by f(x) = 975.06x + 32,906.42, where x is the number…

A: Step 1:Step 2:

Q: 13. (a) Find a number 8 such that if x- 2 < 8, then 4x - 8 < 8ɛ, where ɛ = 0.1. (b) Repeat part (a)…

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Q: -(+2h)+16f (x+h)-30f(x)+165 (x-h)-(-2h) Suppose f"(x) 3 Show that the error is O(h4)

A: It is given that,

Q: x+ 6x +7 f(x) = {-x + 3 5 if x < -1 if -1<x<3 if x 2 3 f(2) = %3D f(-1) = S(-7) = S(3) =

A: The given step function is f(x)=x2+6x+7if x&lt;-1-x+3if -1≤x&lt;35if x≥3

Q: if f(x1,x2) = e-*-*2, 0 < x1 < o, 0 < x2 < o, F(x1, x2) = e-Xie-x2 + e-X2 True False

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Q: f(x) = x²e²

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Q: • prove that y` = = for y= (of (1+x)) 1+x²

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Q: Prove that for integers y=1 the equation 3h-n (2x₁ + x₂ + 4x₂) +3² (~1(2x₁+x₂+.+xn-1)+...+3^-1 (2²₁)…

A: We will use contradiction to prove it.

Q: ab³/2 (7) If x = then log(x) = c2d' %3D (A) log(a) + log(b) - 2log(c) - log(d) (B) log(a) + log(b) -…

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Q: Express the following in the form In(x + a) + ln(x − a) + ln(x² + b), with a, b = N: In(x¹ − 1) = |…

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Q: (x- 1) (x– 2)(x+ 1) (x+ 2)(x- 3) (x+ 3) 2. Let f"(x) = and g'(x) = For what values of x are Az) and…

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Q: If h(x)  =   x  +  1     if x˂  -1                               2  + 2x    if x ≥  -1        Find…

A:

Q: Suppose that the functions g and h are defined as follows. g (x) =x-6 h (x) = (x– 3)(x+1) (5). (a)…

A: Given that gx=x-6 and hx=x-3x+1

Q: Suppose that an = 4" a₁x² + 2a₂x³ + 3a3x4 + 4a4x³. as 00 (i) f(n)x+2 n=0 00 (ii) Σ g(n)x¹+1 n=1 00…

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Q: PROVE THAT  x0.23 = 0.444078 SOLVE [(0.4-0.2)/(0.23-0.2)]=[(0.422845-0.447825)/(x0.23-0.447825)]

A: To prove that, x0.23=0.444078 by solving the following…

Q: . f(x) = 2* DA. O(x²) DB. Ω(x) Dc. O(x²) f(x) = [x][x] (floor of x times ceiling of x) DA. O(x²) DB.…

A:

Q: If f(x) = x*e*, then f"(x) = A 12x²e* B e(x* + 4x?) © e*(xª + 4x3 + 12x²) ex(x4 + 8x3 + 12x²)

A: Given; f(x) = x4ex

Q: e (1? + Зх — 4) dx. 4) d.r.

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Q: x'-x+2 If fx) =ア+7 6. , find f'(x). (5x-1) (A) (3x) (x'+7)(5x-1)-(x'-x+2)(3x) (x+7) (B)…

A: Given query is to find the derivative of the expression.

Q: values

A: We will find the value of x between 0&lt;x&lt;10.

Q: Evaluate the function f(x) = e* + In (x + 6) at 0. (Express numbers in exact form. Use symbolic…

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Q: Evaluate each of the following expressions using the given table of values 2 (a) f(g(-1)) 1 2 (a)…

A: x-2-1012f(x)-10-21-1g(x)210-10The values of different functions at different inputs are given

Q: f(x) = x – 1 m(x) = 3x + 2 h(x) = -4 g(x) = x2 – 5x + 4 4. (m • g)(x) 5. (mof)(x) 6. (g - f)(x)

A: (m×g)(x)=m(x)×g(x)given:m(x)=3x+2 and g(x)=x2-5x+4(m×g)(x)=(3x+2)(x2-5x+4)=3x3-13x2+2x+8

Q: Show that E( X - K )2 = var( X) + [E(X) - K]2

A: var(X)=E(X2)-E(X)2 E(a)=a  where a is constant (a-b)2=a2-2ab+b2

Q: (1) Let A={1,{2},{1,{2}}} (a)True or false: 2 € A, {2} € A, {{2}}CA, {1,2}CA, 3x(x € A^xA)

A:

Q: - Show that f(x)= E ƒ(x), where E is a constant and f(x)= e²x + e2x

A:

Q: Find a general formula for f("). f(x) = (x+4)-1 (Use symbolic notation and fractions where needed.)

A: Given that the function