Theorem: Assume p is an accumulation point of A and assume be T. Then lim f(x) = b, if and only if lim f(rn) = b, n00 for every sequence {rn} of points in A – {p} which converges to p.

Q: Find the roots of the given complex number 1. z^3 = 2 – 3i

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Q: A rectangular tank with a square base, an open top, and a volume of 27,436 ft° is to be constructed ...

A: Let the dimension of the tank be x ft×x ft×y ft. Given, volume=27,436 ft3. ⇒x2y=27,436⇒y=27,436x2 He...

Q: The letters r and 0 represent polar coordinates. Write the following equation using rectangular coor...

A: Introduction: In two dimensional geometry, a point in a rectangular coordinate can be converted into...

Q: Find a remainder when dividing 23490 with 7.

A: We have to find the remainder when dividing 23456 with 7. Fermat theorem:- If p is prime then ap−1=1...

Q: (Q4) Prove that if f : R → R is continuous function, and (n¡)ieN is a sequence of non-zero natural n...

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Q: Q) Let Tright on R ? {(a, o0) : a € R}U {¢, R} . Prove that Tright is toplogy

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Q: The amount of pollutant M in the atmosphere is decreasing with time t according to the formula M = =...

A: If M=f(t), then t is called the input of the function, and M is called the output of the function. T...

Q: A dress-shop owner has 8 new dresses that she wants to display in the window. If the display window ...

A: A dress-shop owner has 8 new dresses.  She wants to display in a window which has 5 mannequins.  So ...

Q: Find distance between point A(1,3) Perpenclicular the line L: 2y =2+X on

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Q: Let z, y, z be digits so that the 9-digit number 5z36y98z2 is divisible by 792. a Without calculatin...

A: Given 9 digit number 5x36y98z2 is divisible by 792. (a) Without calculating x,y explain what is the ...

Q: Are any of the operations used in Gauss’ method redundant? That is, can any of the operations be syn...

A: To determine: If any of the operations used in Gauss’ method is redundant. That is, if any of the op...

Q: Problem (1): Show that there is only one automorphism, the identity function, of Q.

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new ques...

Q: Let Gbe an open set in R". Two points x, Y e G are said to be equivalent if they can be joined by a ...

A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball...

Q: 20. A frog is at the bottom of a 17-foot well. Each time the frog leaps, it moves up 3 feet. If the ...

A: Determine the net distance it moves in every leap. Use the net leaping distance and the fact that it...

Q: Find the Laplace transform of the following: 1) t cosh 2t

A: Find the Laplace transform of the following: 1) t cosh 2t

Q: Let --)-()-0-0 VA vi 9. where cER. What is the only value of c for which the set {v1, vz, V3, V4} is...

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Q: Prove Vr, y E Z, if ry is even and y is odd, then r+y is odd.

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Q: for the following relations on the set A = {1, 2, 3}: R = {(1, 1), (1, 2), (1, 3), (3, 3)}, determin...

A: Given A = {1, 2, 3} R = {(1, 1), (1, 2), (1, 3), (3, 3)}

Q: Which of the following quadratics has imaginary roots? (1) x² +3x – 5 = 0 (3) 2x² – 3x+1=0 (2) x² +6...

A: For a quadratic equation: ax2+bx+c=0, the discriminant is calculated using the formula: D=b2-4ac. I...

Q: Using ɛ-6 argument, prove that f(x) = x-[x] is continuous at all x ERexcept the integers. (Note: [x]...

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Q: Solve the integral equation S" F(x) cos px dx = ' - P.01 4. .Hence prove that o sin?t -dt = %D

A: Given the integral equation is ∫0∞Fxcospxdx=1-p,0≤p≤10p>1

Q: Qchang to Polar and evaluate the double integrals (x*+ xy')dydx 3

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Q: A teacher wants to assign 4 different tasks to her 4 students. In how many possible ways can she do ...

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Q: (a) Create a graph with six vertices of degrees 2, 2, 2, 3, 4 and 5. Construct the matrix of the gra...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Find the difference quotient en-7 for each of the given functions. B. f(x) = 3x + 2 Find the slope o...

A: Solution

Q: Find the Laplace transform of the following: 1) t2 sinh 2t

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Q: Find the Green's function for the boundary value problem d²y/dx? + µ°x = 0, y (0) = 0 = y (1). %3D

A: To find Green's function first we find two solutions of the differential equation using to given bou...

Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation to approximate the...

A: Given: hx=x4 To approximate the values of 34 and 44 using linear approximation of hx. Note: the line...

Q: For f(x,y,z)=3xy+2y+8z - cos(x²+y²–z), the partial derivative fxy(1,2,5)=

A: Given function is fx,y,z=3xy+2y+8z−cosx2+y2−z. We have to find the partial derivative fxy1,2,5. Firs...

Q: Show that the column space of the matrix A is {(x,y.z) E R³:x+y+z=| 1 -1 0 where A =O 1 -1 00

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Q: 3. Solve for fel(r) given that f(x)%3= sinh(3r)

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Q: If 2| <1, the indefinite integral 1+ z14 can be written as a power series , Cna4n-13 + C, with Cn Th...

A: The main objective is to approximate the integration by using power series expansion.

Q: 1. Let f(æ) = { 3æ° /1 – 2a³ x3 – 3x if a 0 Evaluate f(x)dæ 2. Find F' (x) if F(x) = S VE² + Idt. · ...

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Q: Use metaphor/layman's term to explain the Bisection method and how it is being implemented

A: Bisection method: The Bisection method is one of the simplest and most reliable of iterative methods...

Q: A chemical manufacturer sells sulfuric acid in bulk at a price of $100 per unit. If the daily total ...

A: Given that Cx=100,000+50x+0.0025x2. And according to the given information Rx=100x And 0≤x≤7000 a We...

Q: Consider the points A(1, -2,4), B(2, –4, 1), C'(-1, –3, 1), and D(3, 1, –5). (a) Find the volume of ...

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Q: Prove that the only homomorphisms from Z to Z (Z being the ring of integers) are the identity and ze...

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Q: For the function f(x) = v1 +x, let xo = (a) Find the Lagrange interpolating polynomial for f(x). (b)...

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Q: Convert the following symbolic statement into words if s=The sunroof is extra, r=The radial tires ar...

A: Introduction: Two simple statements can be joined together by logical connectivities. As a result, w...

Q: Using Bisection Method, find the real root of the equation f(x) = 3x - V1+ sinx

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Q: There are 4 different Mathematics books and 5 different Science books. In how many ways can the book...

A: Total number of ways that the books can be arranged is 5760

Q: Transform the given improper integral into a proper integral by making the stated u-substitution, th...

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Q: 20. Solve the difference equation y, +Yn-1 = Un +÷Un-1, where un is unit step sequence.

A: Given difference is  yn+14yn-1=un+13un-1 where un is the unit step sequence and is defined as  un=1,...

Q: 9) Find the measure of Angle BÁC

A: Use the result  The measure of the angle formed by tangent and secant outside the circle is half the...

Q: A region is bounded by the curve x = 4y and the line x-y. if the bounded area is rotated about Find ...

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Q: Find the center, length of major and minor axis for ellipse 4x +9y + 24x = 0 Hence, sketch the ellip...

A: Solutions 

Q: Problem 4. Write a function that has a horizontal asymptote at y=2 and vertical asymptotes at z-1 an...

A: For a rational function fx=gxhx vertical asymptotes are given by hx=0 Horizontal asymptote of a func...

Q: II. Which of the following statements are true? Give an explanation for each false statement. (1) Ø ...

A: ϕ is an empty set, that is there is nothing in the set, so no element can belong to it, therefore (1...

Q: What is the result of combining aifferent shapes whetner repeated or altered to create a cohesive de...

A: Given: Different shapes. To find: What is the result of combining different shapes whether repeated ...

Q: Find the Laplace transform of the following: 1. e3t cos 2t

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