
1. (a) Find L4 and R4 for the integral
1 (x sin x/2) dx
Show the setup and round the answer to threedecimal places.
(b) Find M4 for the integral
1 (x sin x/2) dx . Show the setup and round the answer to four
decimal places.
Sketch the approximating rectangles on the graph.
(c) Compare the estimates with the actual value
1 (x sin x/2) dx
10.243 . Which estimate is the most accurate?
(d) Express the integral from...
consider the variation of constants formula where P(t)= a) show that solves the initial value problem x'+p(t)=(t) x()= when p and q are continuous functions of t on an interval I and tg p(s)ds We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image tg p(s)ds
Discrete Math:
Decide whether (p^q)r and
(pr)^(qr) are
logically equivalent using boolean algebra. Show work! Do NOT use
truth table.
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Let X1,...,X10 be a random sample from N(θ1,1) distribution and let Y1,...,Y10 be an independent random sample from N(θ2,1) distribution. Let φ(X,Y ) = 1 if X < Y , −5 if X ≥ Y , and V= φ(Xi,Yj) . 1. Find v so that P[V>=v]=0.45 when 1=2. 2. Find the mean and variance of V when 1=2. 10 10 2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
Let
be an arbitrary function and A
X.
i) Show that A
ii) Give an example to show that in general A =
.
iii) Show that, if
is injective, then A =
iv) Show that, if X and Y are modules;
is a homomorphism of modules and A is a submodule of X such that
ker,
then we also have A =
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Show that
is not uniformly continuous on .
f:R +R, f(1) = x + 2.0 We were unable to transcribe this image
Consider a binomial experiment with n = 15 and p = 0.1. a.Compute f(0) (to 4 decimals). b.Compute f(14) (to 4 decimals). c.Compute P(x 3) (to 4 decimals). d.Compute P(x 4) (to 4 decimals). e.Compute E(x). f.Compute Var(x) (to 1 decimal) and (to 2 decimals). Var(x) = (to 2 decimals) = ( to 2 decimals) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Show that Brewster's Law (where the incident angle i = p ) and Snell's Law together imply that p +2 = 90 degrees. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Please show all work:
Let
If x is odd then
If x is even then
Prove that
is true and then solve it.
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Let T : C([0, 1]) → R be a (not necessarily bounded) linear
functional.
Show that T is positive if and only if
=
(here 1 denotes the constant function [0, 1] → R, x → 1).
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