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Problem 1. Assume that F-(Fi, F2):S-R2 is a function of class C2. Show that if S is parametrized ...
multivariable calculus proofs are needs thanks!!!!! Assume that F = (F1,F2) : S → R2 is...
multivariable calculus proofs are needs thanks!!!!!
Assume that F = (F1,F2) : S → R2 is a function of class C2,
and that F(x)=x for all x∈∂S.
Prove that
Problem 3. Assume that F F(x) = x for all x E S. (Fi, F2):S +R2 is a function of class C2, and that Prove that Fi (-2da +-dy) = Jas a | det DF (x) dA. We were unable to transcribe this image
1. PRELIMINARY DISCUSSION 1.1. Goal. The goal of this assignment is to use Green's Theorem and li...
I need to solve q3. Please write clean and readable. Thanks.
1. PRELIMINARY DISCUSSION 1.1. Goal. The goal of this assignment is to use Green's Theorem and line integrals to prove the following theorem. Theorem 1. Let S denote the closed unit ball in R2, that is, S := {x E R2 : 1-1 Assume that F : S → R2 is a function of class C2 such that F(x) = x for all x E as. Then it cannot...
(3) Let f(t) := (sint)/t, with the understanding that f(0) = 1 (for reasons which should be obvio...
(3) Let f(t) := (sint)/t, with the understanding that f(0) = 1 (for reasons which should be obvious from your study of limits in Calculus 1). (a) Show that ļf(t) 1 forall t. (Note that f is an even function, so you can assume t0. In fact, we will only be concerned with f (t) for t 20 in this problem.) The Laplace transform F(s) of f (t) is therefore defined for all s >0 (b) Show that -1/s <...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = yzi - yj + xk and the surface S the part of the paraboloid z= 4 a2 ythat lies above the plane z = 3, oriented upwards. curl FdS To verify Stokes' Theorem we will compute the expression on each side. First compute S curl F = Σ <0,y-1,-z> curl F.dS Σ dy dπ (y-1)-2y)+z where 3 -sqrt(9-x^2) Σ 3 sqrt(9-x^2) curl F...
Problem 1. Consider the function f(x)- 3.12 show that f is Riemann integrable on [0.2] and use the definition to f...
Problem 1. Consider the function f(x)- 3.12 show that f is Riemann integrable on [0.2] and use the definition to find .后f(x)dr Problem 2. Consider the function -2, zEQ 2, O f(r) = Show that f is not Riemann integrable on 0,1 but s Reemann integrable on this interval. Problem 3. (a) Let f be a real-valued function on a, b] such thatf()0 for all c, where c E [a, b Prove that f is Riemann integrable on a, b...
Problem 1 (11 pts] The independent r.v.'s X and Y have p.d.f. f(t) = et, t>0....
Problem 1 (11 pts] The independent r.v.'s X and Y have p.d.f. f(t) = et, t>0. Compute the probability: P(X+Y > 2). Hint: Use independence of X and Y in order to find their joint p.d.f., fx,y, and then use the diagram below to compute the probability: P(X+Y < 2). y 2 r+y = 2 y . ! 2 0 2-y Note: If X and Y represent the lifetimes of 2 identical equipment of expected lifetime 1 time unit, then...
Problem 3: Recall that the general expression for the vector potential is: A(. ,t).n f įe.war...
Problem 3: Recall that the general expression for the vector potential is: A(. ,t).n f įe.war where tR is "retarded time", t.-t A very long (effectively infinite) neutral wire on the z-axis has zero current before t-to, anda steady current lo is suddenly turned on at t-to in the direction of +2. At a point a distance "s" from the wire, the B-field first becomes nen-zero at t,to+s/c At any time t>, the magnitude of the vector potential can be...
above is the answer, because this is unit step function, and we know initial value is...
above is the answer, because this is unit step function, and we
know initial value is zero, so I can separate the function into two
part just like following q5, and then use d/dt to equate both side.
but I cannot get the correct value, please help me
We were unable to transcribe this imageover Ky(t) ==0) Assume in the following questions that M = 1, D = 2 and K = 2. = e(-(Ki + K2) sin(t) + (Ki...
Definition 1 Denote by Lra the straight line that is perpendicular to the direction [cos(a), sin(a) and at distance...
Definition 1 Denote by Lra the straight line that is perpendicular to the direction [cos(a), sin(a) and at distance r from the origin 0= (0,0). Thus (z, y) is on the line Lra if and only if r cos(a)+y sin(a) r Common choices are r E R and 0 a<. Another potential choice might be r2 0 and -T<asT. Remark 2 The line Lra is a distance r from (0,0) in the direction perpendicular to [cos(a), sin(a)] Consequently, the point...
Definition 1 Denote by Lra the straight line that is perpendicular to the direction [cos(a), sin(a) and at distance...
Definition 1 Denote by Lra the straight line that is perpendicular to the direction [cos(a), sin(a) and at distance r from the origin 0= (0,0). Thus (z, y) is on the line Lra if and only if r cos(a)+y sin(a) r Common choices are r E R and 0 a<. Another potential choice might be r2 0 and -T<asT. Remark 2 The line Lra is a distance r from (0,0) in the direction perpendicular to [cos(a), sin(a)] Consequently, the point...
multivariable calculus proofs are needs thanks!!!!!
Assume that F = (F1,F2) : S → R2 is a function of class C2,
and that F(x)=x for all x∈∂S.
Prove that
Problem 3. Assume that F F(x) = x for all x E S. (Fi, F2):S +R2 is a function of class C2, and that Prove that Fi (-2da +-dy) = Jas a | det DF (x) dA. We were unable to transcribe this image
I need to solve q3. Please write clean and readable. Thanks.
1. PRELIMINARY DISCUSSION 1.1. Goal. The goal of this assignment is to use Green's Theorem and line integrals to prove the following theorem. Theorem 1. Let S denote the closed unit ball in R2, that is, S := {x E R2 : 1-1 Assume that F : S → R2 is a function of class C2 such that F(x) = x for all x E as. Then it cannot...
(3) Let f(t) := (sint)/t, with the understanding that f(0) = 1 (for reasons which should be obvious from your study of limits in Calculus 1). (a) Show that ļf(t) 1 forall t. (Note that f is an even function, so you can assume t0. In fact, we will only be concerned with f (t) for t 20 in this problem.) The Laplace transform F(s) of f (t) is therefore defined for all s >0 (b) Show that -1/s <...
Help Entering Answers (1 point) Verify that Stokes' Theorem is true for the vector field F = yzi - yj + xk and the surface S the part of the paraboloid z= 4 a2 ythat lies above the plane z = 3, oriented upwards. curl FdS To verify Stokes' Theorem we will compute the expression on each side. First compute S curl F = Σ <0,y-1,-z> curl F.dS Σ dy dπ (y-1)-2y)+z where 3 -sqrt(9-x^2) Σ 3 sqrt(9-x^2) curl F...
Problem 1. Consider the function f(x)- 3.12 show that f is Riemann integrable on [0.2] and use the definition to find .后f(x)dr Problem 2. Consider the function -2, zEQ 2, O f(r) = Show that f is not Riemann integrable on 0,1 but s Reemann integrable on this interval. Problem 3. (a) Let f be a real-valued function on a, b] such thatf()0 for all c, where c E [a, b Prove that f is Riemann integrable on a, b...
Problem 1 (11 pts] The independent r.v.'s X and Y have p.d.f. f(t) = et, t>0. Compute the probability: P(X+Y > 2). Hint: Use independence of X and Y in order to find their joint p.d.f., fx,y, and then use the diagram below to compute the probability: P(X+Y < 2). y 2 r+y = 2 y . ! 2 0 2-y Note: If X and Y represent the lifetimes of 2 identical equipment of expected lifetime 1 time unit, then...
Problem 3: Recall that the general expression for the vector potential is: A(. ,t).n f įe.war where tR is "retarded time", t.-t A very long (effectively infinite) neutral wire on the z-axis has zero current before t-to, anda steady current lo is suddenly turned on at t-to in the direction of +2. At a point a distance "s" from the wire, the B-field first becomes nen-zero at t,to+s/c At any time t>, the magnitude of the vector potential can be...
above is the answer, because this is unit step function, and we
know initial value is zero, so I can separate the function into two
part just like following q5, and then use d/dt to equate both side.
but I cannot get the correct value, please help me
We were unable to transcribe this imageover Ky(t) ==0) Assume in the following questions that M = 1, D = 2 and K = 2. = e(-(Ki + K2) sin(t) + (Ki...
Definition 1 Denote by Lra the straight line that is perpendicular to the direction [cos(a), sin(a) and at distance r from the origin 0= (0,0). Thus (z, y) is on the line Lra if and only if r cos(a)+y sin(a) r Common choices are r E R and 0 a<. Another potential choice might be r2 0 and -T<asT. Remark 2 The line Lra is a distance r from (0,0) in the direction perpendicular to [cos(a), sin(a)] Consequently, the point...
Definition 1 Denote by Lra the straight line that is perpendicular to the direction [cos(a), sin(a) and at distance r from the origin 0= (0,0). Thus (z, y) is on the line Lra if and only if r cos(a)+y sin(a) r Common choices are r E R and 0 a<. Another potential choice might be r2 0 and -T<asT. Remark 2 The line Lra is a distance r from (0,0) in the direction perpendicular to [cos(a), sin(a)] Consequently, the point...
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