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Real Analysis
Find the fourier series for the function f(x)= x on the interval 0≤x≤2π ?
Real Analysis
5. You receive an order written for 375 ml of D5W to be administered over 6 hours. Calculate the flow rate of the infusion with an IV set that has a drop factor rate of 20gtt/mL. Additionally, calculate the administration rate in ml/hr.
Real Analysis
If f is continuous on [a, b] and integral a to b of f(x)g(x)dx=0 for all continuous functions g on [a, b] then f is identically equal to 0 on [a, b]
Real Analysis
For each of the following relations, indicate whether they are reflexive, symmetric, and transitive (for example select reflexive and transitive if the relation is reflexive and transitive, but not symmetric).
(a) Let R be the relation on N given by xRy if and only if x divides y.
(b) Let X be a set and let R be the relation "⊆" on . In other words, SRT if and only if S⊆T.
(a) Let R be the relation on N given by xRy if and only if x divides y.
(b) Let X be a set and let R be the relation "⊆" on . In other words, SRT if and only if S⊆T.
Real Analysis
If y=-2x^(3)-3x, determine dy/dt when x=1 and dx/dt=4
dy/dt=?
dy/dt=?
Real Analysis
For each of the following relations, indicate whether they are reflexive, symmetric, and transitive (for example select reflexive and transitive if the relation is reflexive and transitive, but not symmetric). (a) Let R be the relation on N given by xRy if and only if x divides y. (b) Let X be a set and let R be the relation "⊆" on . In other words, SRT if and only if S⊆T. (c) Let S be the set of people in the world. Define R on S by xRy if and only if x likes y (use common sense) (d) Let R be the relation {(1,1), (1,2), (2,2),(1,3),(3,3)} on the set {1,2,3}.
Real Analysis
For each of the following relations, indicate whether they are reflexive, symmetric, and transitive (for example select reflexive and transitive if the relation is reflexive and transitive, but not symmetric).
(a) Let R be the relation on N given by xRy if and only if x divides y.
(b) Let X be a set and let R be the relation "⊆" on . In other words, SRT if and only if S⊆T.
(c) Let S be the set of people in the world. Define R on S by xRy if and only if x likes y (use common sense)
(d) Let R be the relation {(1,1), (1,2), (2,2),(1,3),(3,3)} on the set {1,2,3}.
(e) Let R be the relation on R given by xRy if and only if x−y∈Q.
(f) Let R be the relation on R given by xRy if and only if x−y∉Q.
(g) Let R be the relation on R given by xRy if and only if (x−y)2<0.
(h) Let R be the the relation on R given by xRy if and only if |x-y|≤2
(i) Let R be the relation {(1,1), (1,2), (1,3), (2,1), (2,2),(3,1)} on the set {1,2,3}.
(j) Let R be the relation on R given by xRy if and only if xy∈Q.
(a) Let R be the relation on N given by xRy if and only if x divides y.
(b) Let X be a set and let R be the relation "⊆" on . In other words, SRT if and only if S⊆T.
(c) Let S be the set of people in the world. Define R on S by xRy if and only if x likes y (use common sense)
(d) Let R be the relation {(1,1), (1,2), (2,2),(1,3),(3,3)} on the set {1,2,3}.
(e) Let R be the relation on R given by xRy if and only if x−y∈Q.
(f) Let R be the relation on R given by xRy if and only if x−y∉Q.
(g) Let R be the relation on R given by xRy if and only if (x−y)2<0.
(h) Let R be the the relation on R given by xRy if and only if |x-y|≤2
(i) Let R be the relation {(1,1), (1,2), (1,3), (2,1), (2,2),(3,1)} on the set {1,2,3}.
(j) Let R be the relation on R given by xRy if and only if xy∈Q.
Real Analysis
Compute lower and upper integrals o0f the function
f(x)
=4, 1<=x<=2
=3, 2<x<=4
=2, 4<x<=5
Is this function Riemann integrable on [1,5]? Justify.
f(x)
=4, 1<=x<=2
=3, 2<x<=4
=2, 4<x<=5
Is this function Riemann integrable on [1,5]? Justify.
Real Analysis
Consider the function on [1,5]:
f(x) =
1, x=2
-3, x=4
0, x element of [1,5], x not equal to 2, x not equal to y.
a) Show that for every epsilon greater than 0 there exist a partition P_epsilon of [1,5] such that
L(f, P_epsilon) > -epsilon, and partition Q_epsilon of [1,5] such that U(f, Q_epsilon)< epsilon.
b) Based on part a, prove that f is Reimann integrable on [1,5] and compute the integral.
f(x) =
1, x=2
-3, x=4
0, x element of [1,5], x not equal to 2, x not equal to y.
a) Show that for every epsilon greater than 0 there exist a partition P_epsilon of [1,5] such that
L(f, P_epsilon) > -epsilon, and partition Q_epsilon of [1,5] such that U(f, Q_epsilon)< epsilon.
b) Based on part a, prove that f is Reimann integrable on [1,5] and compute the integral.
Real Analysis
Compute the lower and upper integrals of the function
f(x) = 4, 1<=x<=2
3, 2<x<=4
2, 4<x<=5
Is this function Reimann integrable on [1,5]? Justify.
f(x) = 4, 1<=x<=2
3, 2<x<=4
2, 4<x<=5
Is this function Reimann integrable on [1,5]? Justify.
