Suppose G(r) is the generating function of a sequence (an)o, satisfying G'(r) =rG(r), G(0) = 1. i. Use the ODE to show that G'(0) = 0 and use this information, together with G(0) = 1, to find ao and a₁.

Q: [1] The forward-difference formula can be expressed as h h2 f'(xo) = [f (xo+ h) – f(xo)] f"(xo) f"…

A: Consider the provided question, The forward difference formula is given as,

Q: Suppose that f(-5) = 0, f'(-5) = 4, f(8) = 9, f'(8) = 6, g(8) = -5, and g'(8) = 4. Compute (f o…

A:

Q: Start with an initial guess x = a₁. Then define a2 to be the x-intercept of the tangent of f(x) at…

A:

Q: A plane with equation 2 + ² + 2 = 1 (a, b, c > 0) together with the positive coordinate planes forms…

A:

Q: Suppose h = f ∘ g. Find h'(0) given that f(0) = 6, f'(5) = -2, g(0) = 5, and g'(0) = 3.

A: It is given that

Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 f'(2) = g'(2) =…

A:

Q: Let f(x) = 3x + 1, x, = -1, x, = 0, x3 = 1, x4 = 2, and X5 = 3. Find E f(x,).

A: we have the given the following details   f(x)=3x+1x1=-1x2=0x3=1x4=2x5=3We have to find∑i=15f(xi)

Q: == 3.14. Prove l'Hôpital's rule in the following form. Suppose f(a) = f'(a) = f(n-1) (a) = 0, g(a) =…

A: Given :f(a)=f'(a)=....=f(n-1)(a)=0  , g(a)=g'(a)=...=g(n-1)(a)=0 We have to prove :…

Q: Let g(s) = (5s – 8)*. - Then g'(s) is g'(3) is s! (s),,6 and g''(3) is

A:

Q: Suppose that f is a function with f'(2) = −5. If u is very very close to 0, then f(2 + u) is…

A:

Q: Sketch a graph of a function f(x) that satisfies all of the following. f(-3) = -3, f(-1) = 2, f(2) =…

A: Graph of function using given information

Q: 10- 10 -10

A: Given function is

Q: Sketch a graph of a function f(x) that satisfies all of the following. f(-3) = -3, f(-1) = 2, f(2) =…

A:

Q: 4. Given a function f(x) that is written as f(x) = h' (2) = 4, then f'(2) =? g(x) h(x), if g(2) = 2,…

A: 4. Given a function f(x) that is written as f(x) =g(x)·h(x) , if g(2) =2 , h(2)=-2 ,g'(2)=-3 and…

Q: Let k be a decreasing function such that k) = == O O O O 22 25 N/W 300 8 1/2 and k'(x) = −3x² + 1.…

A: Given thatk be a decreasing function such that  and If g is the inverse of k , we have to find the…

Q: The graph of f (x) is shown in Figure 2.18. Which of the following are true for f as shown in this…

A:

Q: Let f(x) = In[x4(x +9)6(x2 + 4)3]. Find f'(x). f'(x) =

A: Given,

Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 = ƒ'(2) = g'(2)…

A:

Q: Suppose that P(A)=0, P(C|A) =0.006, and P(C'|A')=0.0055 Find P(A∣C).

A: GivenP(A)=0P(C|A)=0.006P(C'|A')=0.0055

Q: If f be the function defined by f (x) = x³ + x. lf g (x) = f−¹ (x) and g (2) = 1, what is the value…

A:

Q: Let f be a decreasing function such that f(0) = 4 and f'(0) = h'(0)=; 3 Oh'(4) = 3 Oh'(4) = 0…

A:

Q: The graph of f is shown in the figure. 6. 4 х 14 -4 -6+ 2-

A:

Q: Problem 6 This extreme value problem has a solution with both a maximum value and a minimum value.…

A:

Q: If f(x) = (3x – 2)(2x + 3), then a. f(– 2) b. f'( – 2) = c. f''(– 2) d. The values of x for which…

A:

Q: f(x) = ex/³; [1₁3]

A:

Q: Suppose P(t) represents the population of a certain mosquito colony, wheret is measured in days. The…

A:

Q: uppose that f and g are functions such that f(5)=3, f'(5)=-2, g(5)=4, and g'(5)=-5. nd h'(5) where h…

A:

Q: Use the Rules of Logs to expand, then find f'(x) given f(x) = ln V. ex X (x + 3)5

A:

Q: Consider the table of vales for the functions r). J ), u() and g'(x): If the function k is defined…

A: Given, k(x) = f(g(x))