Suppose that A and B are sets and f : A –→ B is a function. Fix subsets X,Y C A. Prove that Imf(X) – Imf(Y) C Imf(X – Y).

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A: Let's consider P(n) denotes the number of cannonballs needed to create a pyramid n layers high.

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A: There are four polya's steps in problem solving 

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Q: Use a double integral in polar coordinates to find a such that the volume inside the hemisphere z = ...

A: Given z=64-x2-y2  and cylinder x2+y2=a2 Therefore, the hemisphere intersects the xy plane at z=0 i.e...

Q: 4. Use the definition of the definite integral as the limit of Ricmann sums to compute (Зл — 1) dr. ...

A: We have to approximate the given integral using right endpoint formula.

Q: If a spherical propane tank is filled 80% of its capacity. How many gallons of propane does the tank...

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Q: Evaluate Diffesence Table also identija correct. 24 68 1o 12 14 fa)= 625 625 2401 656|. Corvect By h...

A: Complete the difference table as follows:  

Q: 8. Find the volume of the region bounded by the plane z = 16 and the paraboloid z = x² + y?. (Use cy...

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Q: The Fibonaccis Sequence is defined so that F = F –1+ Fr-2. Given that F12 144 and F13 233, find F14,...

A: Given that  The Fibonaccis sequence is defined. 

Q: Finding the Area Under a Curve In this task, you will practice finding the area under a nonlinear fu...

A: Given : Function: y=20x-x2 . Interval=0,20

Q: a) Expand the binomial (2x – 1)* using the binomial theorem. b) Write the following in closed form (...

A: The given problem is to expand the given exponential function and also to find the closed form of th...

Q: Let the Universal Set, S, have 127 elements. A and B are subsets of S. Set A contains 94 elements an...

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Q: Graph the function f(x) = sin x on the interval [- 7,x), showing the addition of the rectangles asso...

A: The question is about left Reimann sum.

Q: Plot the point given in polar coordinates and find two additional polar representations of the point...

A: Given: 4, -π3 To find: Plot of polar coordinate and additional two representations of the point.

Q: Plot the solid bounded by the paraboloid z = x^2+y^2 and the upper sphere z = √(6-x^2-y^2). Then use...

A: The complete solution is in given below

Q: Complete the truth table for the statement ~S → R. S R -S →R T ? v F ? v F ? v F F ? v

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Q: Homework: Section 9.C Homework Question 10, *MML Only 3.8 Assume an exponential function has a start...

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Q: Finding the Area Under a Curve In this task, you will practice finding the area under a nonlinear fu...

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Q: The equivalent resistance R of two resistances connected in parallel is given by 1. 1 1 Find the equ...

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Q: 3. Let S be the subspace of R' given by S = {(x1, x2, T3, T4) : x1 – 2x2 + 4.x3 – 3x4 = 0} %3D - a. ...

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Q: c) What can you conclude about this series? Select all that applies. O The series converges because ...

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Q: 6. E-Loan offers a 36 month auto loan at 9.25% compounded monthly to applicants with fair credit rat...

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Q: Now assume that both firms are in the market and they make choices over the quantities that they cho...

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Q: Let u = u(x, y), and let (r, 0) be polar coordinates. Then 1 ||Vu|l? = u? +u r2 Use this to compute ...

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Q: Apply the Divergence Test, if applicable, to the series In 2n+5 n=1 Apply the integral test to the s...

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Q: Example 2: Evaluate numerically I= f fxye dydx.

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Q: Suppose z is implicitly defined as a function of x and y by the equation cy z3 – xevz + y sin rz = 3...

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Q: A plane flying horizontally at an altitude of 1 mile and a speed of 480 mi/h passes directly over. h...

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Q: Among real square matrices, which type can ALWAYS be diagonalized by using coordinates with respect ...

A: Let  A be a matrix of a linear transformation T on a finite dimensional(n) vector space V is said to...

Q: 1. Consider the relation < on the set {1,2, 3, 4}. Write down this relation as a set of ordered pair...

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Q: Calculate L4 for f(x) = 84 cos ()

A: Given,           f(x)=84cosx2  over 2π4, 2π2

Q: Which of the following groups are solvable groups: Z/nZ, D8, and S4.

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Q: Per Find the inverse of each function. 1. y = 2x + 1 X: 2441 2. y = -3+* 3. y = x² + 8 X- -3+ +3 t) ...

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Q: 4. Let A be a 3 x 4 matrix and B be a 4 x 5 matrix such that ABx = 0 for all x E R°. a. Show that R(...

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Q: Consider the series Σ (8n - 1) a) Enter an integral whose convergence or divergence is equivalent to...

A: Given: A series, ∑n=1∞18n-12 To find: a) The integral whose convergence or divergence is equivalent ...

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 9t5

A: Here we using Laplace transformation formula .

Q: Use a linear approximation to approximate 32.121. Let f(x)=3x and use the tangent line point at x=2....

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Q: Consider the triangle T with points A = (1,0, 1), B= (1, 1, 2), C = (-1,2, 2). 1. Compute the area o...

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Q: 2. Rotating around a vertical axis: y = 4x -x2, y = 3 and rotated about x = 1.

A: We have to find point of intersection and draw the region bounded , Then rotate the region about x=1...

Q: Give the definctiua of the, hctat matan padet AR Sy Usc yous onswer to Identeta the sze of the Vesal...

A: As per policy question (a) solved.Please re-post for the question (b).

Q: Solve the ifferential equation using Ace Laplace transforms- y"-2s'+9 = 6 xe*

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Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a...

A: We will check whether the given seq is increasing or not   

Q: Evaluate the following integral by changing the order of integration in an appropriate way: SSS2 12x...

A: Evaluation of the triple integral, using order of change of integrals

Q: qu2 .01 ai anoitoni lo oonoupse a od (A oels bnnI.031 moitonl s of 1. Let m*(A) = 0. Prove that for ...

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Q: 7(xe* +e*)sin(xe*)–14sin(x)dx

A: Evaluation of the indefinite integral

Q: Use Pascal's Triangle given below to find the following: 6. 3 8 1 1 1 2 1 3| 3| 1 4 6 1 15 | 10 | 10...

A: We have to find the value using Pascal triangle.

Q: 3y-8 and x2+2y%3D0 is rotated about y-10-D0

A: We have to find the volume of region.