1. Show that if f is a bijection from a set X onto a set Y then f is a bijection from Y onto X.

Q: O Find the general solution of the given system of equations. x-( ). 3 3 -2 -2 x':

A: To find the general of the below system of equations. X'=33−2−2X

Q: Assume a vector field E(p, ø, z)= 3 p sin(4)apt 2 pag is given in free space; assume that z = 0 y2…

A: Given that, Eρ,φ,2=3ρsinφaρ+2ρ2aφ and z=0 (a) to evaluate ∮LE.dl over the contour , given that x1=2,…

Q: 1. Let a and b be elements of a field F. Show that if ab = 0 then either a = 0 or b = 0.

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Solve the system by the method of your choice. 1 X. 1 3 - 2x + y = 4

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Q: 36. How many distinct permutations can be made from the letters of the word STATISTICS?

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Q: Find Df and Duf to:- XZ on the point (,,1) inthe direction of V = 2i -3j+6 K. %3D soLiin ansi- lo

A: Directional derivative of the function.

Q: 4h 2. E+3 (-1)"3 3. E 4. E常 e" 6. 5. 5

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. (a) Find the Taylor series of In(r) about a for a > 0. Your answer should be in sigma notation.…

A: Introduction: A function's Taylor series is an infinite sum of terms defined in terms of the…

Q: It is known that f(1) = 2, f'(1) = -1, g(1) = 0, and g'(1) = 1. If F(x) = f(x) cos cos (g(x) ), then…

A: Given information f1=2f'1=−1g1=0g'1=1 And function is Fx=fx⋅coscosgx Now, differentiate…

Q: Use the currency exchange rates in the table for the following question. Dollars per Foreign per…

A: Solution :-

Q: Odsek Styty Starting with the reciprocal equation f(x) =- %3D describe the transformations in words…

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Q: Use Spherical coordinates to calculate the triple integral of f(r, y, z) over the given solid. (a)…

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Q: In the following problem, begin by drawing a diagram that shows the relations among the variables. w…

A: Given that,  w=-2x2-2y2+2z2                       (1)z=x2+2y2…

Q: Rewrite the given system of linear homogeneous differential equations as a homogeneous linear system…

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Q: 3. Let f(x) =1+x+x² + x³ + æ“ + x³. (a) definition of Taylor polynomials. (b) Find T3(x), the Taylor…

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Q: 2. Use the MVT to show • Prove that the derivative of f(x) = k, on [a, b], where k is constant, is…

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Q: 3. Determine the fourier series that represents the function as follows; T = 8, A, = 0 (Symmetrical)…

A: Given T=8, A0=0Yt=-1-4 to 0Yt=10 to 4

Q: A carpet is to be installed in one room and a hallway, as shown in the diagram below. At a cost of…

A: To find the cost to the carpet area when cost per square meter is $14.50 . And the figure is given .

Q: Make your own symbolic statement that construct a truth table for it Example: p^[~(p↔q)]

A: Given statement is p∧~p↔q. We have to construct a truth table for the statement p∧~p↔q. The truth…

Q: U he sinylexe meliad to slue the pro subjeet to てx+メ 2 x, + X2 < 12 Xi + Sx2< 12 XI,X2 ZO

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Q: Use spherical coordinates. Evaluate (6 - x2 - y?) dv, where H is the solid hemisphere x² + y? + z? <…

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Q: An RLC circuit is modeled using the differential equation below with initial value i(n) = 20 t?i' +…

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Q: Find the general solution to the following nonhomogeneous differential equation using the method of…

A: Solution of second order differential equation, by using method of undermined coefficient

Q: 4. The exact simple interest on P 450 for the period from January 10, 2004 to a "specific date" is P…

A: Given, Principal ,P= P 450 Rate ,R= 18% Simple interest ,S.I.= P 70.22 To find: a) Specific date…

Q: Find the absolute maximum and minimum of the function f(x,y) = 8y? - 72x - 4 over the closed region…

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Q: (c) all f such that f(3) = 1 + f(-5); (d) all f such that f(-1) = 0; (e) all f which are continuous.…

A: (c) S = { f : f(3) = 1 + f(-5) }       Let f, g € S.        Then f(3) = 1 + f(-5)…

Q: A laboratory uses 700 white mice each year for experimental purposes. It costs $4 to feed a mouse…

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Q: an eigenvector, find the corresponding eigenvalue. (a) u = |0 (b) v (c) w = |0 [3 0 2 0] 1 3 10 0 1…

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Q: Let sin A = 3 5 with A in QII and sin B = −  8 17 with B in QIII. Find sin(A + B), cos(A + B), and…

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Q: A rain gutter is being installed on a home that has the dimensions shown in the figure below. At a…

A: Here given that a=9, b=12, c=17 and d=30 Here we imagine two rectangles of side a , d and (c-a) , b…

Q: Find a basis for and the dimension of the subspace W of R*. w = {(3s - t, s, 2t, s): s and t are…

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Q: Write the given system in the form x' = P(t)x+f(t) x' = y+z, y' = z+x, z' = 5y-7

A: Given system is x' = y + zy' = z + xz' =5y -7z Take x, y, z are dependent variables and depend on t…

Q: Suppose that f is a bounded non-negative measurable function. Show that there exists a decreasing…

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Q: 2² + 2 Determine a simpler function g(x) such that y = x +2 asymptotic to y = g(z) as a → +00 or x →…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts…

Q: 1. (a) ( Find the Taylor series of In(x) about a for a > 0. Your answer should be in sigma notation.…

A: Given function fx=lnx Taylor series for fx about a for a&gt;0 is  fx=fa+x-af'a+x-a22!f''a+… Now,…

Q: 3. Use the MVT to show that the function f(x) = 1/x³ is uniformly continuous on the interval 3,00).…

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Q: Describe the graph of the equation. r = -9i + (1 – ²)j+ tk It is a parabola in the plane x -9, with…

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Q: Find the exact values of sin(?/2), cos(?/2), and tan(?/2) for the given conditions. sec ? = −  5 4;…

A: Given that,  secθ=54,  and  180°&lt;θ&lt;270°

Q: cirrF Find the equation to the sphere through the circle x + z? = 1, x + 2y + 3z = 4 and the origin.…

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Q: Use Secant Method to find the root of x³ + 3x² – 1= 0 between [-3, -2] accurate to five decimal…

A: We have f(x) = x3+3x2-1 f(-2) = -23+3-22-1 = 3 x1 = -2 f-3 = -33+3-32-1 = -1 x0 = -3

Q: Graph the region bounded by r = 3 - 6 sin 0.

A: The polar coordinate system is a two-dimensional coordinate system in which each point on a plane…

Q: Solve the second-order difference equation Y=2=7Yt=1 + 10Y, = 4t + 8t

A: We solve  Yt+2 -7Yt+1+10Yt=4t+8t........(1)

Q: Show that if α and β are Dedekind cuts, then so is α + β = {r1 + r1 : r1 ∈ α and r2 ∈ β}.

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Q: B. Two coins are tossed and a ball is drawn from a bag containing a yellow and a red ball a. If L is…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: does there exists   ______such that if n is divided by 5 the remainder is 2 and  if   ?

A: We have to check whether there exist n such that if n is divided by 5 then remainder is 2. Let if n…

Q: Use the composite Simpson's rule with step length h=0.5 to determine 1= [ (2x - - 3x2 + 4x – 1)dx,

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Q: . For n, m 20 and n # m, show S' T.(z)Tm(7). VI- -dr 0 This is called the orthogonality relation for…

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Q: Question 2 |Consider the following Initial Value Problem -y – y' = 2 – 1, y(4) = 2. a) 1 Use Euler's…

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Q: Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for…

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Q: (a) Find the general solution of the given system of equations. )= :). 5 -9 x': 2 -4

A: Introduction: The system of differential equation is represented as x'=Ax This system is homogeneous…