1. Consider the distribution Tylo]-)dx where f(x)H(x), and H() is the Heavi- side function. Find ...
(a) Let h() be defined by 1. h(x) h2, х > а where h h2 and a are constants. Find the first and second derivatives of h in the distributional sense (b) What is the third derivative of |x| in the distributional sense.
(a) Let h() be defined by 1. h(x) h2, х > а where h h2 and a are constants. Find the first and second derivatives of h in the distributional sense (b) What is the third derivative...
Find moment generating function of geometric distribution f(x)=p*q^(x-1), where x=1, 2, ... and use it to find EX and DX (i.e. find the first and the second moments).
Consider the function f(x)-5x -x-3 and complete parts (a) through (d) (a) Find fix + h) (b) Find fkth) fs) (c) Use the above answer and the limit definition of the derivative to find the derivative of the function f (d) Find the value of the derivative of f when x-1 (a) fx+h)- Simplify your answer. Do not factor) fx+ h) fx) Simplify your answer Do not factor.) c) f(x) E (d) The derviative f(1) elfo Simplify your answer)
1.Z=f(x,y)=6x+7y where i) x=g(x)=x^2 y=h(x)=x^4 and ii )x=g(x)=x and y=h(x)=x^3. Please calculate Total derivative by applying this formula dZ=Zx dx/dx +Zy dy/dx
7.7 EXERCISES 1. Let 1-(x) dx, where f is the function whose graph is shown. (a) Use the graph to find L2,R2, and M2 (b) Are these underestimates or overestimates of 1? (c) Use the graph to find T2. How does it compare with /? (d) For any value of n, list the numbers .L. R, M. T, and I in increasing order 0 1 2 34x
7.7 EXERCISES 1. Let 1-(x) dx, where f is the function whose graph...
Consider the function
f(x)=x22−9.
(1 point) Consider the function f(x) = 9. 2 In this problem you will calculate " ( - ) dx by using the definition Lira f(x) dx = lim f(x;)Ar i=1 The summation inside the brackets is R, which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub- interval. r2 Calculate R, for f(x) = -9 on the interval [0, 3] and write your answer as a...
f(x+h)-f(x) Find the difference quotient h where h = 0, for the function below. f(x) = 2x-3 Simplify your answer as much as possible. f(x + n) - f(x) h Х $ ?
3. Consider the function f :D → R given by f(x) = the following x - x. With the a (a) Find the derivative of f. Is the function strictly increasing, dec (b) Find the second derivative of f. Is the function strictly concave neither? (c) Suppose D = [0, 1] find the maximum and the minimum of f. (d) Suppose the domain D = (0,1), find the maximum and the min (e) Suppose the domain D = [0, 0),...
The standard Cauchy distribution has cumulative
distribution function
F(x) = 1 + 1 tan−1(x) 2π
where −∞ < x < ∞.
1
a. Find the probability density function of X.
b. FindxsuchthatP(X>x)=0.2.
Question 7: The standard Cauchy distribution has cumulative distribution function F(x) = + tan-1 (x) π where-00< 00. We were unable to transcribe this image
f(x+h)-f() Find the difference quotient h where h# 0, for the function below. F f(x) = 2x² + 2x Simplify your answer as much as possible. h G х ?