Write an equation for the ellipse. Type the left side of the equation in the box below. (x-3)² (+1)² 36 4 =1

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Q: dx (a²+x²)z 1. S- 3

A: We can a valve the given integral by using the substitution x= a tanθ.

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Q: Find the integral of ([sin(x)]^6){[cos(x)]^7)dx from x=0 to x = pi/2. 14/1001 15/2002 16/3003…

A: …

Q: Use l'Hopital's rule to find the limit. (√x² + 4x - x) 51) lim X→00

A: Given; Limx-infinity [sqrt(x2+4x) -x]. Repost the next question.

Q: The linear approximation at x = and where B is: 0 to 1 X is A + Bx where A is:

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Q: A farmer wants to fence a rectangular area of 242 square feet next to a river. Find the length and…

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Q: 10. y' + y cotx = 5ecos x, when x = 1, y = -4 ANSWER KEY: 10. y sin x + 5e cos x =

A: Please see the below picture for detailed solution.

Q: [x = t - 1 Q.1 Verify that the lines L₁ y=1-t lz=1-t and find the distance between them. and [x = 2t…

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Q: Solve the initial value problem. d²s_ dt² 34) -128cos (8t), s (0) = 6, s(0) = 8

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Q: y = 14. If u +4 u-4 and U= √x + x 10 dy , find dx when x=4.

A: This question can be solved using the concept of derivatives.

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A: Given; dr/dt =4 inches per minute and h=6r.

Q: III. Eliminate the AC 8. до Gex + сче-х + Сухе аех Cex ·X

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Q: Verify the Divergence Theorem for the vector field and region: F = (3x, 5z, 3y) and the region x² +…

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Q: What is the maximum slope of a tangent to the function f(x) -x³ + 4x - 2? ==

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Q: 3T and answer the following questions. Consider the follow series: 0 (-1) 1 a) Use the Ratio Test to…

A: This is a problem related to series and sum calculation. Please follow the procedure given below.

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A: We need to find equation of hyperbola.

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Q: Using the Runge-Kutta method of order 4, find y for x = 0.1, 0.2, 0.3 given that dy/dx = xy + y²,…

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Q: ← Find an equation for the hyperbola described. Graph the equation. Center at (-7,-6): focus at…

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Q: In general, the profit function P(x) of a product or service is defined as the difference between…

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Q: Find the transfer function, G(s)=C(s)/R(s), corresponding to the differential equation, d³c d3 +3.…

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Q: Find the function represented by the following series and find the interval of convergence of the…

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Q: Use an appropriate test to determine whether the following series converges. 8!!! Σ 9 3 k=1 ³√k…

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Q: 4) Find the solution of y'= 2(2xy) passing through (0,1).

A: Given, Equation  y'=2(2x-y) passing through a point (0,1).

Q: Evaluate the limit: lim 5 = x → 2

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Q: g. Let g(x) = log(1 + 2x²). Tick all of the following statements that are true. 00 is in the range…

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Q: The area of a circle is increasing at a constant rate of 88 square meters per second. At the instant…

A: The answer is given below:

Q: Consider the following piecewise function ƒ : R → R 3.2³ 7.x 8x²730 f(x) = Indicate which of the…

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Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: 23) (-4,-24) 30- 20+ 10+ to.p -10+ -20- f(x) = x3 + x² - 6x -30 (3, 18) 2 Find the area enclosed by…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Use the Ratio Test to determine if the series converges. M8 k=1 %*x Select the correct choice below…

A: Ratio Test : Consider the given series ∑k=1∞ ak .and L = limk→∞ ak+1ak , then(i)If  L<1, then…

Q: Calculate Sc(x + y) ds, where C is the rectangle formed by de x=0, x=4, y= -1 and y=1

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Q: Using polar coordinates, evaluate the integral Se sin(x² + y²)dA where R is the region 4 ≤ x² + y² ≤…

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Q: Find the breakeven point of the following functions: C(x)= 4x +4 R(x) = 6x Approximately (2, 12)…

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Q: b

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4 3 1…

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Q: Evaluate the integral. esin−1 3x √1-9x² 32) dx

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

Q: 5. The motion of the shock absorber is modelled by the function, h(t) = e-0.5t sint. 3 a) Identify…

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Q: es and state values of 0 that produce the entire graph s the entire graph of the parabola?

A: We have to convert in polar form from the given Cartesian curve (parabola)

Q: Graph f(x) = 2-√√5-4x Use the transformation of graphs techniques. Show all transformations. Label…

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Q: Solve the initial value problem. dr-csc² 50 cot 50, 42) de 43) dy dx 3 (7) - y(0) = 6 (6 + x)2'. = 3

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Q: Which of the following represents a linear equation that begins at 5 and increases by 8 at each…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

A: We will find the required.

Q: For which of these line equations is the WRONG slope given? 3x + y = 15; m = 3 4y = 16x +…

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Q: Consider the function f(x) = 5-6x², -5 ≤ x ≤ 1. The absolute maximum value is and this occurs at x =…

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