Show all your work. Let f(x) = x 5 e x 3 (i) Use the Taylor...

Show all your work. Let f(x) = x 5 e x 3 (i) Use the Taylor series for e x around 0 to find the Taylor series for f(x) (ii) Use (i) to find f (20)(0), f (21)(0), f (22)(0), f (23)(0)

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milcah answered 2 years ago

5. (a) Let f : R \ {−1} → R, f(x) = x+1. Show that f...

5. (a) Let f : R \ {−1} → R, f(x) = x+1. Show that f is injective, but not surjective. (b) Suppose g : R\{−1} → R\{a} is a function such that g(x) = x−1, where a ∈ R. Determine x+1 a, show that g is bijective and determine its inverse function.

Show that "f(x) = x^3" is continuous on all of ℝ

Problem 3. Let F ⊆ E be a field extension. (i) Suppose α ∈ E is...

Problem 3. Let F ⊆ E be a field extension. (i) Suppose α ∈ E is algebraic of odd degree over F. Prove that F(α) = F(α^2 ). Hints: look at the tower of extensions F ⊆ F(α^2 ) ⊆ F(α) and their degrees. (ii) Let S be a (possibly infinite) subset of E. Assume that every element of S is algebraic over F. Prove that F(S) = F[S]

Let be the following probability density function f (x) = (1/3)[ e ^ {- x /...

Let be the following probability density function f (x) = (1/3)[ e ^ {- x / 3}] for 0 <x <1 and f (x) = 0 in any other case a) Determine the cumulative probability distribution F (X) b) Determine the probability for P (0 <X <0.5)

f(x)=e^x/(3+e^x) Find the first derivative of f. Use interval notation to indicate where f(x) is increasing....

f(x)=e^x/(3+e^x) Find the first derivative of f. Use interval notation to indicate where f(x) is increasing. List the x coordinates of all local minima of f. If there are no local maxima, enter 'NONE'. List the x coordinates of all local maxima of f. If there are no local maxima, enter 'NONE'. Find the second derivative of f: Use interval notation to indicate the interval(s) of upward concavity of f(x). Use interval notation to indicate the interval(s) of downward concavity...

Let E and F be independent events. Show that the events E and F care also...

Let E and F be independent events. Show that the events E and F care also independent. Hint: Start with P(E∩Fc) =P(E)−P(E∩F) and use the independence of E and F.

Please use excel and show all work and formulas. (I will give your work a like...

Please use excel and show all work and formulas. (I will give your work a like if you do this) Size (1000s sq. ft) Selling Price ($1000s) 1.26 117.5 3.02 299.9 1.99 139.0 0.91 45.6 1.87 129.9 2.63 274.9 2.60 259.9 2.27 177.0 2.30 175.0 2.08 189.9 1.12 95.0 1.38 82.1 1.80 169.0 1.57 96.5 1.45 114.9 What are the p-values of the t test (for the slope estimate) and F test? What is the coefficient of determination? What is...

(a) Let <X, d> be a metric space and E ⊆ X. Show that E is...

(a) Let <X, d> be a metric space and E ⊆ X. Show that E is connected iff for all p, q ∈ E, there is a connected A ⊆ E with p, q ∈ E. b) Prove that every line segment between two points in R^k is connected, that is Ep,q = {tp + (1 − t)q | t ∈ [0, 1]} for any p not equal to q in R^k. C). Prove that every convex subset of R^k...

3. Let X = {1, 2, 3, 4}. Let F be the set of all functions...

3. Let X = {1, 2, 3, 4}. Let F be the set of all functions from X to X. For any relation R on X, define a relation S on F by: for all f, g ∈ F, f S g if and only if there exists x ∈ X so that f(x)Rg(x). For each of the following statements, prove or disprove the statement. (a) For all relations R on X, if R is reflexive then S is reflexive....

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere. a) Find a...

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere. a) Find a so that f(x) is a probability density function b)What is P(X<=1)

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