What does the equation x = 5 represent in ℝ2? a point a line a plane a circle What does it represent in ℝ3? a point a line a plane a circle

Q: Given polar equation: r = 4 + 8sin0, 0 ≤ 0 ≤ 2π Please explain what interval the inner loop of the…

A: The inner loop of the limacon is defined by,Therefore,

Q: 6 5 4 3 2 y 0 1 ¦ y = f(x) 1 2 3 5 6 7 8 9 Enter each answer as a whole number (like -4, 0, or 253)…

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Q: The graph of a rational function fis shown below. Assume that all asymptotes and intercepts are…

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Q: 11.Find the area under the curve y=sin2xcosx for the given limits; sketch the area. Hint: integral…

A: y= (sin2x)(cosx)We have to find area under curve y from π to 3π/2

Q: 24. Find the equation of the plane that contains the points (5, 0, 4), (1, 3, 3), and (3, 1,3).

A: Given dataPoints of a plane,

Q: If cos(0) sin(20) + sin(0) cos (20) do.

A: Note:-As per your demand we solve the long trigonometric integration problem Given integral

Q: 35. lim x² - 16 x-4 4 - x

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Q: Evaluate the following indefinite integral. Le egy 4 + el8y You can use "C" for any needed constant…

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Q: ₂. "Derine straight line equation is space X-X y-y. Z-Z₁ b C

A: The equation of a straight line in three-dimensional space can be derivedusing vector and parametric…

Q: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius…

A: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.The radius…

Q: obtain differential equation for the family of lines whose intercepts are equal

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Q: Find the function value. f(x) O = x2+7 x + 6x 2300 11 23 88 -; f(4)

A: We have :f(x)= (x2+7)/(x3+6x), We have to find f(4)Also given:f(x)=4-6x2We have to find f(-7)

Q: Sketch a graph of f(x) = = -5 -4 -3 -2 -1 Clear All Draw: 4 3 2+ H -1 -2 -3 -4 3 N|W 2+1 2 3 10 .

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Q: 8. One-sided and two-sided limits Use the graph of g in the figure to find the following values or…

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Q: 1) Find the derivatives of the following functions: a) x³e b) sin(x³ + 2x) I c) 1+x²

A: We are authorized to answer three parts at a time, so we are answering the first three parts. Please…

Q: a. Use the substitution usin x to evaluate the integral I sin: sin æ cos xda b. Use the substitution…

A: Given that a integration and we solve this problem by using general property of integral.

Q: Convert the Cartesian coordinate (-6, 2) to polar coordinates, with 0 ≤ 0 0 r= 2√10 0 =

A: To convert the Cartesian coordinates to polar coordinates,with .

Q: 6-6. Using any method we have studied thus far, find the derivatives of the following functions: (a)…

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Q: Simplify (3 — 5x)4(x²y4)³z6 2–³ (27x6)¹/³ (3 — 5x)−³y4z−²

A: Given Expression

Q: A yeast culture is growing at a rate of W'(t) = 0.4e0.12t grams per hour. Find the area between the…

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Q: Your rich aunt Hannelore is setting up a fund for victims of math tests. The fund will pay $10000…

A: To calculate the amount of money that needs to be invested today to ensure the fund lasts forever,…

Q: b. Use the substitution u = cos x to evaluate the integral I sin sin a cos adr

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Q: Find a particular solution of Yp(x) = y'+2y+y = e [(5 - 2x) cos(x) (3 + 3x) sin(x)] -

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Q: Use the graph of H shown to the right to find the limit. If necessary, state that the limit does not…

A: A graph of the function is given.The aim is to find the limit of the function  at .

Q: In this question I just don’t understand the part where it says therefore and they get a system of 2…

A: We need to find how to get system of equation.

Q: 4.) Find the slope of the tangent line to the graph of y = arctan3x at the point (2, arctan6)..

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Q: Find the area of the region between the curves: y = √√√x and y = x² from x = = 0 to x = 2

A: y=x and y=x2 from x=0 to x=2

Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

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Q: T 1 m Į 1-1/² -y=1 -2 m x

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Q: Solve § (12x + 4)eª dä using Integration by Parts. Jse u = 12x + 4 and v' = eª.

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Q: (a) x²ex

A: the function given is As per the rules, we are supposed to answer the first question, and the rest…

Q: Jane took 15 min to drive her boat upstream to​ water-ski at her favorite spot. Coming back later in…

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Q: For Problems 41-44, let h(x) = f(g(x)) and k(x) = g(f(x)). Use Figure 3.21 to estimate the…

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Q: The graph of the function f(x) is shown below. It consists of a semicircle and two straight line…

A: The given figure

Q: Solve the initial value problem y(t) = dy dt - y = 3et+ 12e4t, y(0) = 9

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Q: The differential equation dy dx 18 y1/6 +9x2y¹/6 has an implicit general solution of the form F'(x,…

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Q: Calculate the integral approximation Sg for 6 √₂ 72²1 dx. S8 =

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Q: Write the standard form equation of the parabola with directrix = 4 and vertex at the origin. Enter…

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Q: An oil tanker breaks apart and starts leaking. As time goes on, the rate at which the oil is leaking…

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Q: 3. Use the graph of h in the figure to find the following values or state that they do not exist.…

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Q: Given vectors , and w in the picture below Draw - using Triangle law -8 -7 -6 -5 -4 w -3 -2 W -1 8 7…

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Q: 2) Find the following indefinite integrals: a) f(5x³ - cos x) dx b) dr c) fe+1 da

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Q: 5 -4 -3 -2 -1 9 J -4 3 2 1 -2 -3 -4 S z p-q= 0 X P Find the components of the subtraction p F q of…

A: Vectors in component form

Q: 4. If you are given $30 every year on your birthday, and put it straight into a bank account that…

A: Principal amount Interset rate According to Recursion formula:    where

Q: Find the divergence of the vector field F = div F = r

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Q: 1.3 Question 1 Differentiate each of the following functions using the Product, Quotient or Chain…

A: Note: I am using product rules for differentiating each function as asked.

Q: decide the derivative of asin(bx),step by step.

A: Given function

Q: Use the method of Lagrange multipliers to solve this exercise. Hercules Films is also deciding on…

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Q: Question Determine the for the following function: f(t) = 9t7-7t+1 that is deffined F(s) = {9t²-7t…

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Q: how do you evaluate the following integral without dividing it into two parts? ∫(0 to ∞)  ​x−2dx

A: To evaluate the following integral.