sopved
in sheet
Show that g() = z?e" is not an antiderivative of f(1) = 2xe", but h(x) =...
Let f, g E H(C) be such that |f(z)| < \g(z)| for any z e C. Show that there exists a E D(0,1) such that f(z) = ag(z) for any z E C. (Hint: consider f/g and be careful with the zeros of g.)
1.For x ≥ 0, let f(x) = 2xe−x^2 Show that f is a density function. 2. Find the cumulative distribution for the density in the preceding exercise. 3. Find the pth quantile of this distribution.
Added the formulas, thank you!
Approximating derivatives f(z +h) - f(z) f(x)-f( -h) f(x + h) - f(x - h) Forward difference Backward difference Centered difference for 1st derivative s(a) (3) 2h t)-2e-bCentered diference for 2nd derivative (4) 2 2. Write a short program that uses formulas (1), (3) and (4) to approximate f(1) and f"(1) for f(x)e with h 1, 2-1, 2-2,.., 2-60. Format your output in columns as follows: h (6+f)() error (öf(1 error f error Indicate the...
Find an antiderivative F(x) of f(x) = 2 − 3e^x so that F(1) = 4. show work
Find the most general antiderivative of f(x) =(1/3x) − 2sec^2(x/2)−e^−2x+3 SHOW ALL WORK
11. LetF(x, y) - (2xe), x + x-e)) and let C be the quarter-circle path from A to B in Figure 18. Evaluate 1-φ F . dr as follows: (a) Find a function f (x, y) such that F- G + V f, where G (0, x). (b) Show that the line integrals of G along the segments OA and OB are zero. (c) Evaluate I. Hint: Use Green's Theorem to show that B (0,4) A (4, 0) FIGURE 18
4. Let F be a field. Prove that for all polynonials f(x), g(x), h (z) є FI2], if f(x) divides g(x) and f(z) divides h(r), then for all polynomials s(r),t() E Fr, f() divides s()g(r) +t(x)h(r).
4. Let F be a field. Prove that for all polynonials f(x), g(x), h (z) є FI2], if f(x) divides g(x) and f(z) divides h(r), then for all polynomials s(r),t() E Fr, f() divides s()g(r) +t(x)h(r).
Find the most general
antiderivative of
SHOW ALL WORK
-2.6+3 2 sec f(x) = () e 3.0
please explain, not just an answer. No cursive please.
Suppose that we define a function f(x) in a piecewise manner - f(z) () for x < a and f(x) = h(x) for x > a. Here, assume that g(z) and h(z) are differentiable functions. Show that f is differentiable at a if and only if f(a) g(a) and f'(a) g'(a).
Suppose that we define a function f(x) in a piecewise manner - f(z) () for x a. Here, assume that...
e2 3 does not have a complex antiderivative on CV 3. (a) The continuous function f(z) = 0 (b) The continuous function g(z) does not have a complex antiderivative on C 1 + 1리-
e2 3 does not have a complex antiderivative on CV 3. (a) The continuous function f(z) = 0 (b) The continuous function g(z) does not have a complex antiderivative on C 1 + 1리-