5. Find the critical point or points for each of the following autonomous system. Then match each pair with its phase portrait on the next page. dx d- + 4y +3 = 2x - 2y - 4 and Critical point(s): Matching graphic: FIGURE 6.1.

Q: d) The number of vertices of degree 4 is. e) The sum of the degrees of G is.

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Q: Q2 FILL IN THE BLANKS. No justification is required. Let G be the following graph: 9. 10 11 12 13 14...

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Q: Q3) Find the limit for the following function by using L'Hopital's rule: x- sin x lim x3

A: We have to find the limx→0x−sinxx3 by using L'Hospital's rule. L'Hospital's rule is defined an follo...

Q: What is the general solution to the differential equation (2xy – e")dx + x(x – e')dy = 0 ? 2y – x2 +...

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Q: Minimize F(y, u) = f¿u²(t) dt under ý = -2y + u with y(0) = 1, y(1) = 0. Is your solution unique?

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Q: sin 4x 1. f(x) : complete the table. Show your solution. 2 0.8 0.5 0.1 0.01 0.001 0.0001 f(x) sin 4x...

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Q: -号。 - 4X u (x,o) =3 e 2 , ニ0 y2 Ansl ux,y) = 34(メ+) Ans.l ucx,y) 3 e %3D

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Q: Apply the differentiation rules of a "quotient": ôn, (n ôn2 n Or a differentiation of a product of t...

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Q: What is the general solution to the differential equation (e*y² cos(y) + x)dy + (e*y² sin(y) – y)dx ...

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Q: Find the points in the complex plane (if any) where f is analytic. z2 +1 z # -1 f(2) = z +1' 3 -1

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Q: b) For a set X = {1, 2, 3, 4}, let P be the partition {{1,3}, {2, 4}}. The partition P induces a rel...

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Q: : 2 2. X- -r

A: We know that ∫a2-x2dx=xa2-x22+a22sin-1xa+c

Q: In ARTE,TA bisects ZRTE, M2RTA = (3y – 4)º, and MLETA = (4y – 17)º. What is t measure of ZRTE? A. 13...

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Q: z = f( a, b, d, c), write the exact differential of the dependent variable

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Q: Question 5: Find the winning strategy for a game of sprouts that starts with 5 dots.

A: We have to find the winning strategy for a game of sprouts that starts with 5 dots.

Q: A die is rolled thrice. Combination Not Combination

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Q: Find the trung of the followir series given tl

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Q: 5. Find the number of non negative solutions to x + y + z = 21. With the conditions that x 2, z > 4...

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Q: 2 Suppose V is finite-dimensional and dim V > 1. Prove that the set of noninvertible operators on V ...

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Q: 13. Sketch a graph for a polynomial that is degree 4 with 3 x intercepts and a positive leading coef...

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Q: SHORT ANSWER QUESTIONS. No justification needed. Consider the Hasse diagram of the following partial...

A: Solutions 

Q: Consider the ODE with general parameters b, a, I a'(t) + bæ(t) = at²(1+ sin(qx(t)) Dimensional homog...

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Q: Q5/ Find the limits : 1- limp-0 3 V3h+1+1 x-1 2- lim-1 Jx+3-2

A: We have to evaluate the limits of:limh→033h+1+1limx→1x-1x+3-2

Q: 1. Suppose that f is an infinitely differentiable function (that is, all its derivatives exist and a...

A: For part (d) we perform Integration by Parts on the integration in part (c) and then generalize the ...

Q: Find the determinant of the given matrix. You must show all working. You will get no marks for simpl...

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Q: FILL IN THE BLANKS. No justification is required. Let G be the following graph: 10 12 13 14 15 16 17...

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Q: Solve for the value of r: P(7, r) = 840 %3D

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Q: f(x) = S^ sinh 2tdt

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Q: d) Let X = {1,2,3, 4}. Define a binary relation R on subsets of X by ARB if and only if A and B have...

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Q: H.W:- Selve The lincar SysTems O1.7X-3 O 1.7 3.2y= 8-1 0.4x+ 112y= -2

A: The solution to the system of equation is defined as the values of the variable that satisfy the equ...

Q: Let (fn) be a sequence of real valued functions defined by fn(x) = cos(x) n By definition, show that...

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Q: - Find the number of non negative solutions to x + y + z = 21.

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Q: A = 3 2 4 5 -2 4 | -3

A: Solution

Q: Show that following Matrix is an idempotent Matrix A=5 ーマ

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Q: 1- Solve the following systems linear differential equations (by elimination) dx = -9y, (a) dt dy = ...

A: (a)Given that, dxdt=-9ydydt=-4x Now we solve this system.  

Q: 2+ye*y Which of the following is the general solution to the differential equation y' = 2y-xe*y 2y –...

A: Given y' = 2+yexy2y-xexy

Q: Q4 Let f : R →R be the function defined by 1 f(r) = = a) Is f is one-to-one? If yes, then explain wh...

A: An one- one  function is a function that maps distinct elements of its domain to distinct elements o...

Q: 3. Consider the system of first order ODES (in matrix form)

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Q: A =  3i - j + 2k B = 2i + j - k  C = i - 2j + 2k solve for a.) (A x B) x C b.) A x (B x C)

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Q: Given the graph below, evaluate the following limits: y = b

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Q: \How many ways can Mr. Cinco distribute 12 different books among 4 students (A, B, C, D) such that s...

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Q: The flow F of a certain liquid in a thin pipe is given by F = k P R4, where R is the radius of pipe,...

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Q: O Find Fourier Cosine transform of: CoS X oa

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Q: Q6) Find y' for the following: 1. += 1 y 2 2. хз — уз — у %3D1 - уз — у %3D 1

A: 1. Write the equation in terms of y.

Q: 3. Find the inverse Laplace Transform of the g

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Q: 2) Se* dx

A: Given: ∫x5exdx

Q: 27. Let A be a set and let f: A A be a function. For x, y E A, define x ~ y if f(x) = f(y). (a) Prov...

A: This is a problem of set and function.

Q: Find the round-off error of the following using 5 significant digits: 1 1. 3 2. tan 150 3. 1 — п 4. ...

A: Question number 4:   11531153  ≃  4.86294Round off error = 115 3 - 4.86294                          ...

Q: 3. What are the elements of the sample space S = {r|Vr² – 4x – 5, r 5}? (a) (0, 00) (c) (-00,0) (b) ...

A: We have the sample space, S=x|x2-4x-5,x≤-1, x≥5

Q: a bc If det A =| d ef = k find the value of the given determinant. ghi T1.0: 2d 2e 2f a b g+ 2a h+ 2...

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