Convert each pair of polar coordinates to rectangular coordinates 1. (2,315 degrees) 2. (1, 315 degrees)

Q: sin² x lim 0-x X

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 2) For f(x, y, z) = xe²yz. (a) Find the gradient of f.

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Q: sec x = Let f(x) + x³e² - log₂ (5x + 1) + 1 x² √T Using the derivative rules learned in our course,…

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Q: 1. Evaluate the given integral Q. -2 2y-2 -K² Q Jo 1 = (xy-1) dx dy

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Q: Evaluate the definite integral. (7x² - 6x +9) dx 0

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Q: 1 1 So (²₁-2²-₂) dx xx+1 x+2.

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Q: d. lim+ In 1000 X X5

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Q: Evaluate the definite integral. 3 12√/5y + 1 dy 12√/5y + 1 dy = (Simplify your answer.)

A: Here is the solution:

Q: (1, -2) (a) The curve with equation y2 = x³ + 3x² is called the Tschirnhausen cubic. Find an…

A: We have to find the tangent equation and draw the graph.

Q: The points R(-1, 1, -3), S(3, -3, 6), T(0, 0, 10), and U(2, 4, 7) are the vertices of parallelogram…

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Q: FIND THE AREA OF THE REGION BOUNDED BY THE FOLLOWING CURVES: 1. y = x(x-3), x = 0, x = 5 2. y =…

A: Given

Q: Physical Applications of First-Order Differential Equations A body at a temperature of 50° F is…

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Q: Without using the graph, determine all inflection points of a + x².

A: For inflection point , set f''(x)=0.

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of…

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Q: There are five men and three women in a room. How many committees of 4 people can be chosen from the…

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Q: f cos √2x dx

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Q: The first derivative of the function y = 3x cannot be solved using implicit differentiation. Select…

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Q: dw dw For the functions w= - 4x² - 2y2, x= cost, and y= sint, express as a function of t, both by…

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Q: 1. Evaluate the given integral Q. J[(y - 2x) dA, R where is the region bounded by x = 0, y = x, x =…

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Q: () 2 1- (x+6) (x+2) 2

A: The given integral is:…

Q: Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the…

A: We have to calculate the area using left end right end and mid point methods.

Q: 1) Find a power series representation for the function and determine the interval of convergence.…

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Q: 4 0 dx 1+ √x

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Q: Given: f(x) = 10-X g(x)=x² + 4x-2 Find and simplify (9°F)

A: Given query is to find indicated composite function.

Q: 2 3/2 √₁² (4- x²) ³/² dx

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Q: Find the length of the are of the function x² = 4y from x = -3 to x = 3.

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Q: cos(x) = 1/2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 12. Find the integral of S (x². √(x² + ² =) dx

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Q: 4. Evaluate the following limits. a. lim X→→→+** 2x 3x² b. lim c. lim -3/x X In5 x x²

A: This is a problem related to limit calculation. Based on the general formula and concepts we will…

Q: Find the differential dy: y = sin(x√³). Ody = COS cos (T√²³) [2√T™- 2 O 0 O (E) None of these…

A: A detailed solution is given below.

Q: 1 x² dx So √4-x²

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Q: y=√√√x 0 Figure A 12. Consider the region in Figure A. Its area, using [f(x) - g(x)]dx, is

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Q: The graph of y=f(x) is shown. Draw the graph of y = -f(x). 17 Ex X 3

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The cost in pesos of manufacturing x pairs of pants in ABC Tailoring is given by C(x)=1500+3x+x^2…

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Q: Find the inverse of the function on the given domain. f(x) = (x-5)^2, [5,00) f-1(x): =

A: The solution is given in the next step.

Q: dy dx X2 (1+y2)

A: Let's solve given diffrential equation.

Q: 1. Evaluate the given integral Q. = [] [²³² Q L L (x - y) dx dy

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Q: Find the integral offsec²x dx tan x

A: This is a problem related to integration. based on the general formula and concepts we will answer…

Q: Given: g(x) = x² + 4x=2 Find and simplify (g°g)

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Q: An open-top rectangular box is being constructed to hold a volume of 400 in ³. The base of the box…

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Q: fx ax dx

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Q: Solve the system of differential equations. x₁' = 3x1 - 1x₂ ¸x₂' = 1x₁ + 5x2 x₁ (0) = - 11, x₂(0) =…

A: This is a problem related to solving system of linear differential equation. Based on the general…

Q: For each graph, choose the function that best describes it. (a) (b) (Choose one) (Choose one)…

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Q: Find the derivative of a. (e(sin2x))/[In(cos2x)]2

A: We have to find out derivative

Q: Evaluate the integral. 34 1 8- dx

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Q: Find the derivative of 4Inloge*

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Q: 5. Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3 Then the area…

A: We know  that the area under the graph of a continuous function f (x) between the vertical lines x =…

Q: A forest has a population of lynx and a population of rabbits. Let x represent the number of lynx…

A: Let's solve given diffrential equation.

Q: 3 If f *¸9 (2) dx = -5 g(x) dx = -2 and Find the value of 3 15 -5 g(x) dx 15 g(x) dx = 9

A: Solution of given question is written in below steps.

Q: 1) Find the radius of convergence and interval of convergence of the series. Show All Your Work.…

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