Consider the region depicted in the following figure. Find the area of R. -1 YA 4- 3+ 2 1 0 -1. f(x) = √x g(x) = 2/1/2 - 1/21/2 1 2 3 X

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A: Since we are given with multiple number of question and our guideline is solve first question only…

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A: We need to calculate the distance between the point Q3,1,7 and the plane 2x-6y-z=3 without using the…

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A: The limit is evaluated below.

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A: According to our guidelines, we can answer only one question or three subparts of a question. Other…

Q: Find all critical points of the following function. f(x,y) = 10x²-5y²

A: Please see the below picture for detailed solution.

Q: -2- 0 y = g(x) 4 7 x

A: To evaluate the integral.

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Q: Given compute the following integral. Provide your answer below: -6f(x) dx = = 9 [² f(x) dx = 2,…

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Q: 28. For each of the following equations, find the most general function N(x, y) so that the equation…

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Q: Find f'(x) for f(x) = - 8A√x - 5Bx⁹ where A and B are constants. Completely simplify any fractions.…

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

Q: SULWAY 5. x- 7. dx 9. dt In Problems 7-16, obtain the general solution to the equation. dy -y-e³x =…

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Q: 9. (x²-x+y) dx - x dy = 0 10. (2y² + 2y + 4x²) dx + (2xy + x) dy = 0

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Q: Use the comparison theorem to compare Enter your answer using either ≤ or >. F = = [₁* (√x + I + 2)…

A: We will use comparison theorem to compare the given two Integrals.

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Q: The pH can be calculated using the equation pH = -log(H"), where H" is the hydronium ion…

A: We can find the hydronium ion concentration as below.

Q: cise (a) e volume of the solid formed by revolving the region about the x-axis 01 he region is…

A: To find the volume of solid revolving around x axis using disk method

Q: 01 √ √(x + y + -1 -1 (x+y+1)dxdy

A: This question is based on double integration.

Q: QUESTION 6 Which of the following functions are separable? Of(x,y)=In(xy) f(x, y) = x² + y f(x, y) =…

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Q: 3. f(2x + 3)² dx

A: I have stated the used formulas in the solution

Q: Use Linear Approximation to estimate the quantity 1 80.5

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Q: Find the minimum and maximum values of the function on the given interval by comparing values at the…

A: Find critical points by putting derivative of given function equal to zero

Q: 13. 2ny(8- y³/2) dy A) 4² (14 — y³/²) + C 7 2my 7 (14-y3/2) + C C) B) T² (14+y³/2) + C 7 D) 4²…

A: 13. The given integration is: ∫2πy8-y32dy To evaluate the given integral.

Q: 2. Find the equation of the line tangent to the circle x² + y² + 6x - 2y - 15 = 0 at the point…

A: Here the given circle is , x2+y2+6x-2y-15=0 We need to find the tangent to this circle at the point…

Q: (Simplify your answer. Type an exact answer, using radicals as needed.) b. y = (Type an exact…

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Q: eliminate the arbitraty constats of the differential equation y = C1e^2x + C2xe^2x a. y” + 2y’ + y =…

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Q: Write a recursive formula for the geometric sequence an given below. 10,10/3,10/9,10/27,10/81,…

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Q: Given that the graph of f passes through the point (1,9) and that the slope of its tangent line at…

A: Slope of the  tangent line to the  curve  y = f(x) is f '(x)

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) xy - 25 lim (x, y) → (5, 5)…

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Q: 3 1. f ³√x² dx

A: Solution : Given that integral is

Q: doesn't this mean there are no critical points

A: Given the function fx,y=10x2-5y2

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A: Hee, to evaluate the given integral we have to rewrite the rational function.

Q: Compute the curl of the following vector field. F = (4x²-3y²,5xy,5z)

A: We have to find out solution

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Q: A-Find the intercepts, the symmetry for the polar equation r = cos20 am draw it.

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Q: Consider the points A=(1,2,3), B=(-2,1,0), and C=(0,3,1). Adding the vectors, find 2AB+3AC.

A: To find 2AB +3 AC

Q: Find an equation of the plane tangent to the following surface at the given points. zexy; (1,0,1)…

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Q: Find the derivative. G(t) = sinh(ln(t))

A: Topic = Derivative

Q: Evaluate: AT -dx B. 이집 는 d 를

A: Evaluate the integral ∫0πxsinx1+cos2xdx