10 -34 Evaluate the integral and check your an= iating.

Q: Find the following limits if they exist. 1. 2 3. lim x→+0 5x – 7 8x 4x +1 lim X +2 +x + 27 lim -7 2 ...

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Q: Suppose that f is a bijection and fog is defined. Prove: (i). g is an injection iff f o g is; (ii). ...

A: Solution :-

Q: dr cos(t)r(4-r); r(0) = 1.

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Q: - The circle x +y 1, this mean :- a- C= 0,0, R-2 b- C= 0,0, R-1 c- C-1.1, R-0

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want...

Q: Ito Processes The drift and volatility of Ito processes are general functions dx=a(x,t)dt+b(x,t)dz. ...

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Q: Robert wants to buy a sports is on sale for 25% off. If the price is $35 and sales tax is he sale pr...

A: In this question, the concept of percentage is applied. Percentage When computing the percentage of ...

Q: Find the solution of the following second order differential equation d²y(x) dy + x +x2 y(x) = 0 dx2...

A: Given: The second order differential equation, x2d2ydx2+xdydx+x2y=0, where y=yx   To determine: The ...

Q: Find modulus and argument of: a. (5-7i)(8+5i) b.  (√3 +i)/(√3 -i)

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Q: Assignment Problem. Maximize Profit     Machines Worker 1 2 3 4 A 12 15 11 14 B 10 1...

A: Since, it is a maximization problem, we first subtract the element of the table from the maximum ele...

Q: y implication, P implies Q, the contrapositive of the implication is logically equivalent to P impli...

A: Introduction: a proposition or theorem formed by contradicting and swapping the subject and predicat...

Q: Question 1: Find the Nim-sequence of the subtraction game with subtraction set S= {1,2,5, 7 }

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Q: di L- + Ri = E dt i(0) = io L, R, E and io are constants.

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Q: Solve the following differential equation by using Laplace transform y" = 5, where y(0) = y =0 %3D

A: Introduction: The Laplace transformation of the derivative of a piecewise continuous function ft is ...

Q: nsider the differential equation z' = (e" – 1)(x - 3)(5- a) • a) Find the equilibrium points. b) Gra...

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Q: A rectangular page contains 65 cm? of print. The top and bottom margins of the page are each 0.5 cm ...

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Q: Evaluate the integrals. If the integral diverges, answer "diverges." 375. dx

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Q: dy \ Find for dx et dt

A: In this question, the concept of the fundamental theorem of calculus is applied. Fundamental Theorem...

Q: 3. To defeat Electro, Spider-Man needs to connect all of the pylons (vertices) in the graph below, w...

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since th...

Q: f a car valued at R255000 depreciates on a reducing balance method at an interest rate of 12.5% p.a ...

A: Given that: Time period = 7 years Interest rate = 12.5% per annum  Current value of the car = R2550...

Q: [ Question 1] The function f(t) is defined as f(t) = {," le-2t t>0 otherwise Compute the 1-norm, 2-n...

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Q: Is the series 22"31-" convergent or dive n=1 Co

A: Introduction: We know that the series an=∑an converges only when L<1, diverges when L>1, Where...

Q: Define f : [0, 0) →R by f(x) = x. Find a function g: R → R such that gof is one-to-one, but g is not...

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Q: Use synthetic division and the Remainder Theorem to find the indicated function value. f(x) = 3x-20x...

A: We will use synthetic division and remainder theorem to answer the given question.

Q: Consider a set of integers from 1 - 10. G = {1,2,3,4,5,6,7,8,9,10} Answer the following questions: ...

A: (i). Given G = {1,2,3,4,5,6,7,8,9,10}

Q: If f(t) = t – 5 and g(t) = t² – 3t + 3 then g(f(2)) =

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Q: A 1-i

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Q: Use the recursive definition of summation, the triangle inequality, the definition of absolute value...

A: To Show 

Q: 12 If a, x and y are three non-zero and mutually non-parallel vectors, and th are given by b=x-(x-â)...

A: Introduction: The dot product between two non-zero vectors a^ and b^ are expressed as a^·b^=a^b^cosθ...

Q: 6. (a) Write the following in reduced row echelon form.. Determine (b) a basis for and (c) the dimen...

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Q: Accepting n calculate the following expression: 1/2 + 2! + 3/4 + 4! + 5/6 + 6! + 7/8 + 8! + ... + n/...

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Q: Q4. Find the homogeneous solution for the given D.E using the Power Series method y" = x² y

A: Introduction: A power series solution is related to a differential equation. When the coefficients a...

Q: prove that le besque outer mea sure pt is countably Seb-additive.

A: This is a problem of measure Theory.

Q: Ql find chromatic number of

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Q: xy cos.x f(x, y) =+3y²

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Q: 3. Use the permutation and combination formulas to prove the following. (a). For all integers n 2 3,...

A: Given n≥3, n€ Z (integer ) We have to prove that P(n, 3)+2P(n, 2)=nP(n, 2)

Q: (d) Give an example of functions f: A → B and g: B → C, such that go f is onto, but ƒ is not onto. (...

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Q: 4.Use Lagrang interpolation method to find f(1) based on the following data: -3 2-1 3 ソ=f) 1 2 4 8

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Q: Fred is considering three job offers in advertising. A full-time position as a coordinator that pay...

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Q: A 600 pound object hangs from two cables with angles below the horizontal of 0 25 and ø = 47 respect...

A: We can use Lamis theorem to find the tension in the cables. 

Q: Use mathematical induction to prove the following: 2 1+8+27+·..+ n³ n(n+1) %3D 2

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Q: e of 4,7,1

A: Introduction: A sequence is an arrangement of numbers in a specific order. A series, on the other ha...

Q: 9. Let V be the set of all ordered pairs of real numbers, and consider the following addition and sc...

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Q: Exercice 3 : Solve the first order PDE: Uz + 2u, + (2r - y)u = (2a +3xy-2y)(x+2y) %3D

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Q: Q\ Find the absolute maximum and minimum of f(x) = csc(x) on [ %3D max(x) - min(f(x)-1 max(f(z)- min...

A: Introduction: A function may have a maximum or minimum value of the domain of definition. Suppose, o...

Q: = (1- t)y ,subject to the dt dy 1. Use Euler's Method to solve the differential equation initial con...

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Q: following differential equation: y" + 4y + 4y = e* cos I

A: Introduction: The higher order linear differential equation can be generalized as andnydxn+an-1dn-1y...

Q: If in an AP the sum of m terms is equal to n and the sum of n terms is equal to m .then prove that t...

A: Let us consider the AP a, a+d, a+2d, a+3d,...... The nth term is obtained as  an=a+(n-1)d The sum of...

Q: he directional derivative at the point po (1,2) toward the point pa(-1, from the point po to point p...

A: In this question, the concept of the derivative is applied to find the directional derivative. Deriv...

Q: Suppose that population of the world now is 6 billion and that its doubling period is 35 years. (a) ...

A: The exponential growth of a population can be modeled as Pt=P0ert Where Pt is the population size af...

Q: QAFind dx dt x In(x)/1+ (In(x))Z

A: Introduction: Another method for applying the chain rule of differentiation is the u-substitution fo...