The continuous image of a connected set is connected. That is, if X is connected and f : X–→ Y is continuous, thenf [X] is connected.

Q: Fs (X | proof: HolWo

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Q: Problem 1.58 Check the divergence theorem for the function v = r? sin© î + 4r² cos e ê + r² tan 0 @,…

A: (1) Solution:- Using the volume of icecream cone shown in figure

Q: Find the arc length parameter along the curve from the point where t = 0 by evaluating the integral…

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Q: For an election with four candidates (A, B, C, D) consider the following preference table: NUMBER OF…

A: Solution :-

Q: Evaluate the following limits. cos x – 1 3. lim I-0

A: To evaluate the given limits :-

Q: Find the vertical and horizontal asymptotes. f(x) = -15 -10 -5 5. 10 -2 -4 -6p Step 1 -7x We are…

A: Solution

Q: Find the largest eigen value for the matrix 1 2 A= 5 4 with x" (0) =(7/17 1)

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Q: Question 3.1. Let's think of the set of n-by-n matrices as R by using the matrix entries as…

A: Given: A set of n by n matrix in Rn2 D⊂Rn2 be the subset whose matrices have zero determinants.…

Q: a. Give an example for a commutative ring without identity. b. True or False: Every ring is a group.

A: To find the given questions :-

Q: cos t- sint sint+ cost j, N= - cost- sint cos t- sint j, and K= 1 Find the binormal vector B and…

A: If N and T are unit normal and unit tangent vector respectively then binomial vector  B=T×N If s is…

Q: 2tan x- x lim, -1 2х -sin " x,

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Q: Cornsideing the Laurent series foro S(x) = Which Sin c serterd is aut cand converges what is which…

A: Solution: Since sin(z) has a simple zero at π, the function sinz(z−π)  extends to be analytic and…

Q: Consider The system -31 a) Find a fundamental matrix for thisgs tem ) Find the solu ti'en of the…

A: This question related to system of ode.

Q: 3s+2 l(s-1)(s-2)) a. 5e2t - 8et 3t+2 d. (t-1)(t-2) b. 3 sin t + 2е2t e. Зtet + 2е2t с. 8e2t - 5et

A: L-11s-a=eat.

Q: Find the moment of inertia of the area bounded by the given curves with respect to the specified…

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Q: If L[S(t); p]= 5(p), the Theorem f(u) du; p P

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Q: Use Shell Method to find the volume of the solids of revolution described in each item. Find the…

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Q: A. POWER SERIES SOLUTION OF DIFFERENTIAL EQUATIONS 2. y"+2xy'+5y = 0

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Q: One windshield wiper is 50 units long and is affixed to a swing arm which is 80 units long from…

A: Here, Top of the windshield wiper is 80 unit long from pivot point. Bottom of the wiper is…

Q: ) Consider The system <-3 Find a fundamental matrix for thisgs ten ) Find the solutien of the syetem…

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Q: Consider sets A and B with |A| = 14 and |B| = 19. a. How many functions f : A → B are there? b. How…

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Q: A small generator burns two types of fuel low sulfur and high sulfur to produce electricity. For one…

A: Here we will form a linear programming and solve it graphically to find optimal value for x and y…

Q: - Find the sum of the given series. 1 1. 1- 3! 1 1 5! + ... 7!

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Q: f(t) RIN RIN

A: Here the graph of function is combination of line segments . using the formula for equation of line…

Q: Theorem 11: Let f(t) and g(t) be two functions of class A and let L[f(p);1]= f(t) and L"[E (p);t] =…

A: Using the definition of laplace transform. Changing the order of integration and corresponding limit…

Q: Find the work done by F(x, y) = (x, Y) over the curve r(t) = (e' cost, e' sin t) (x² + y?)3/2 from…

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Q: 4. Consider the following function: 2. -2 < x < -1 f(1) = {r, -1<r<1 1<r<2. 2-I, (i) Sketch the…

A: The graph of f is sketched as shown below.

Q: (i) Sael-²dz, where C is the anticlockwise unit circle |2| = 2. (ii) ſadz, , where C is the…

A: As per our guidelines we supposed to answer only three subpart in case of a multi part question.

Q: Consider symmetric equations of lines х-1 4 = = 2 - y = z and l2 = x = -1, = 2 3 Find: equation of…

A: The given lines are                   l1 : x-12=2-y=z and                l2 : x=-1, y-23=z-12

Q: The effectiveness of a movie commercial depends on how many times a person sees it. After some…

A: Given that effectiveness of a movie depends on how many times a person watches it. The equation is…

Q: what is k ( Q.) ? and why ?

A: Here we use given theorem and definition.

Q: Express the syllogism “All Greeks are Mortal, Socrates is a Greek, Therefore, Socrates is mortal” in…

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Q: Give a reflection about the movie entitled "The Adventures of a Mathematician."

A: Among the many individuals taking part in the Project, there was even the Jewish mathematician of…

Q: Find Soe-=*+u° (cos 2xydx+sin 2xydy), where C : a² +y² = R².

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Q: Find the interval of convergence for the follov ing power series E(coth n)x" n=1

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Q: dzdyde 74 灣彩

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Q: Find the GCD of 284 and 40 using the Euclidean Algorithm.

A: .

Q: 9. An anagram of a word is a rearrangement of its letters (each of the letters must be used exactly…

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Q: If X is a finite dimensional vector space and (e,) is a basis for X, show that an inner product on X…

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Q: 3. Find the Laurent series of f(2) = Log () for |2| > 1.

A: Given function: f(z)=Logz-iz+i To find: Laurent series for f(z) for |z|&gt;1

Q: 6. A solution contains 2.12 moles of NaCl dissolved in sufficient water that has 1750grams mass.…

A: Solution: Given,   moles of solute(Nacl) = 2.12 moles               Mass of solvent (water) = 1750 g…

Q: Q4: (A) Prove or disprove each of the following 1. Every prime ideal is maximal. 3. The cancellation…

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Q: 27 Consider the vector a = -9ị- 3j. (a) Find â. (b) Find the vector b in the direction of a with a…

A: To find unit vector we find the magnitude of vector . To find vector b neglect the negative value of…

Q: Question 3 Express in polar form el14 + 943 - ( 8-j6)/j² Answer must be in polar form (i.e.…

A: Solution-:

Q: The Education Department will apportion a budget of P1,300,000 to six state universities based on…

A: Standard divisor = Total student populationTotal budget = 97,4501,300,000 = 0.075 (rounds to three…

Q: a. s2 +6s+25 s2 b. (s-1)3 7 C. s4 6. 8. s3 s2 S

A: To find:  inverse Laplace of the given functions. Please post the multiple questions separately.…

Q: x- sin x+y) dA

A: The given problem is to evaluate the given double integral over the given region R enclosed by the…

Q: -a (1) Let a, b, t E R, and a + b # 0. A = a b What is the expression of e4t? What are the…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Show that the function f defined by 1, (x, y) = (1, –1) f(x, y) = { x2 + y (x, y) # (1, –1) x + y is…

A: Given function is fx,y=1,           x,y=1,−1x2+yx+y  ,x,y≠1,−1 . We have to show that the given…