Apply Green's Theorem to evaluate the integral (-5y² dx-5x² dy), where C is the triangle bounded by x=0, x+y=1, and y = 0. с $(-5y² dx - 5x² dy) = (Type an integer or a simplified fraction.)

Q: ƒ(x) = x+2 х 8 ²-1 Which of the following statements is TRUE? Ofis continuous at x = 0. Of is not…

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Q: Evaluate the line integral [x(1 с where C is given by the line r(t) = (1 + 3t, 2t), 0≤ t ≤ 1. x(1 +…

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Q: Find each limit. Use oo or ∞o when appropriate. 2x - 10 (x-10)² (A) lim f(x) X-10 f(x) = (B) lim…

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Q: What is the slope of the tangent line to the graph of x^2 - xy + 3y^2 -2x + 4y = 17 at (5,1)

A: We have to find the slope of the tangent line to the graph of x2 - xy + 3y2 - 2x + 4y = 17 at (5, 1)…

Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

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Q: Jamie and Marlene are having an ice skating contest. They skate along a long, straight track and…

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Q: The left, right, Trapezoidal, and Midpoint Rule approximations were used to estimate same number of…

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Q: ra a²-y² L". Sve²=v² a²-x²-y² . (x²z+y²z + z³) dzdxdy a²-x²-y²

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Q: 1: Evaluate the integral 3x - 1 (x + 4)(2x - 1) I -dx.

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Q: Which one is an improper integral? O 6 sin(x-5) x-5 S₁º O none O 6 sin(x-5) x-3 O S 6 sin(x-5) x-7…

A: Improper integral:- An improper integral is a definite integral that has either or both limits…

Q: 18 (x² +9) (x+3) -dx

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Q: a. b. dx x+2x³ In S is Inx In 2x² + 1| + C X C √ √2x² + 1 + ₁ C. d. In|2x² + 1 1 + C In x + In|2x² +…

A: Given problem:-

Q: 2 +81 1/s(3² +9) ²0 ds

A: The given integral is (s4+81)/[s(s2+9)].

Q: c) I following 1. Determine whether the integral is convergent or not. 10 [." : 6 dx x-6 Vx

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Q: Calculate the first three partial sums of the series. S₁ S N' 11 = S3 = Σ n = 1 n+4 Use the sequence…

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Q: 23. Given the triangular numbers 1, 3, 6, 10, 15,... Find the 7th and 8th term of the series. a. 26…

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Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A: We have to find the area of rectangle increasing

Q: 5. Find the area bounded by the polar curve r = 4cos30.

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Q: Find dx dx 0.4 0.4 -3.3x-4+5x -4 -3.3x 5x ...

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Q: 2) Find the indefinite integral by using the method of partial fractions: 3x+5 x²-9x+18 S- -dx

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Q: A particle moves along a line with a velocity v(t) = 1² + 2t - 8, measured in meters per second.…

A: Given thatvelocity vt=t2+2t-8To find : The total distance the partical travels from t=0 to t=3…

Q: Which one is a suitable substitution for the following integral? S -x²+4 x ○ x = 2 sec(t) O x = 4…

A: According to question,Given Integral,Let I = ∫-x2 + 4x dx

Q: Region R is bounded by the graphs of C₁ : x = y + 1 and C₂: x = 3 - y² as shown in the graph below.…

A: Given: Region R is  bounded by the graph x=y+1 and x=3-y2 as shown in question. USE: cylinders…

Q: 2. Find the limit algebraically by factoring the expression first. lim x-10

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Q: The integral 9 [² 1 x - 1 dx

A: NOTE: Refresh your page if you can't see any equations. .

Q: Which value is the average rate of change for f(x) = √x + 1 o the interval (0,3)? 13 0 -1 -3 3

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: For the given functions f(x) = − 9x², g(x) (1) (fog)(x) = (2) (gof)(x) = (3) (ƒ ○ ƒ)(x) = (4)…

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Q: 4. Graph the equation: f(x) = -3, 4, 1/² x + 1²/₁ x<-2 -2 ≤ x ≤ 1 1 < x≤ 4 -3 - 5+ 4+ 1 + 3+ 2+ 1…

A: f(x) = -3 , x &lt; - 2 x -3 -5 -7 f(x) -3 -3 -3 f(x) = 4 , -2 ≤ x ≤ 1 x -2 0 1 f(x) 4 4…

Q: Sx -1 xtan xdx

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

Q: A company is planning to manufacture snowboards. The fixed costs are $400 per day and total costs…

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Q: An equation of the plane passing through A (1,-1, -1), B (1,0,2), and C (-1,-1,-5) is: 2x+3y-z = 0…

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Q: Find the derivative of the following function given

A: Our Aim is to find the derivative of the functions given below:-y=sec2 (x)-tan2 (x)  -(i)

Q: Which of the following statements must be true? 1. If f is differentiable, then II. If f is…

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

Q: = The x-coordinate of the point of inflection on the graph of y 5 0 10 3 - 3+5 +2

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Q: The parametric equations of the line that passes through A(-3,5,9) and B(-4,-7,2) is: x=-3-t,…

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 8…

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Q: Find the angle between the vectors in radians and in degrees. (Round your answer for part (a) to…

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Q: Bob, Trinity, and Roger are painting their living room. Trinity takes twice the number of hours that…

A: This question can be solved using the concept of time and work.

Q: Find all vertical and horizontal asymptotes of the graph of the function. (Enter your answers as a…

A: This question is based on vertical and horizontal asymptote.

Q: f(x) = 0 x = 0. At what value of x is the function given above, discontinuous? Ox=3 x+2 x² −1 8…

A: We need to choose correct option.

Q: Evaluate fcot (x) cos²x dx

A: The given integral: ∫cotxcos2x dx.We need to evaluate the above integral.

Q: 1 好好 0

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Q: Based on the given graph, determine the zeros of the function and note multiplicity (even or odd).…

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Q: Find the radius of convergence, R, of the series. Σ n = 1 R = | 1 Ο μ 2 5 8.. · (3η – 1) Κ Find the…

A: The solution is given below

Q: Use an appropriate test to determine whether the series converges. 1 2 3 26² 27² 28² By the + + +…

A: According to question,Given series,1262 + 2272 + 3282 + ........

Q: Evaluate f dac x²-x+2

A: We can evaluate the integral as below.

Q: 11. Determine whether the given quadratic function has a maximum value or a minimum value, and then…

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Q: Determine X(S) expressed as a rational polynomial with simplified numerator and factored denominator…

A: According to question,Given Data,xt = t2 + 2e-2t + sin 3t ut