Use Green's Theorem to evaluate the line integral of F=<3y+1, 4x²+3> over C which is the boundary of the rectangular region with vertices (0,0),(4,0),(4,2) and (0,2), oriented counterclockwise.

Q: Find the equation of tangent line for the curve f(x)=e³x at coordinate (0,1).

A: Given: fx=e3x

Q: The length and width of a rectangle are measured as 40 cm and 30 cm, respectively, with an error in…

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Q: The value of the definite integral 3 [² (3x² Jo 0 is (3x² - 2x + 4)dx

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Q: Convert the rectangular equation to polar form x² + y² = 9 (solve) rsino = 9 Option 4 O r=3 Option 2…

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Q: 3. fx³√1 + x² dx

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Q: an = arn+1 an arn-1 Option 4 The general term of geometric progression is an=arn a" = arn-1 Option 3

A: Topic = Series

Q: In the find and prove of lim”→0 (x³), how and what should be defined in terms of ? A. 8 = min {1, §}…

A: This question is related to Limits, we will solve it using given information.

Q: Let à = 5j + k and b -2i+j+2k. Find - 3ā – 3b.

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Q: Consider the double integral f(x,y)=(x²+y2) 3/² over the region R where y is bounded between 0 and…

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Q: 3. (a) Solve the differential equation (x+1) ª¹ = y +e³(x+1)² . dx (b) Form the differential…

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Q: Complete the parametric equations for the line where the planes 8x + 11y + 4z 13x + 2y + 3z = 5…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: Evaluate the following integral. √144-16x² dx

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Q: Given the curve of y=6-x² and y=x+4. Sketch the graph for -3<x<3. State the intersection points…

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Q: Consider the following. 2(x-8)² + (y - 6)² + (z − 5)² = 10, (9, 8, 7) (a) Find an equation of the…

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Q: * The differential equation 2ydx-(3y-2x)dy=0 is Exact homogenous and linear Exact and linear but not…

A: The answer is given below:

Q: Question [ a) [1 b)' 1. : Evaluate 6 1₂° ₁x + 2 ): If Show all your work. then find f(x). c) [ graph…

A: a)∫26 (x+2)x-2 dxLet    x-2 = z2      implies     dx =  2z dzx=2   ⇒ z =0x=6  ⇒ z= 2The integral…

Q: Prove that 2 Sin X dx 1 + cotx + cos x It tan X cos 2 x

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Q: Use partial fractions to find the power series of the function: ∞ n=0 5æ + 53 (x − 2)(x + 5)

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Q: Consider the equation below. (If an answer does not exist, f(x)=x²-x-In(x) (a) Find the interval(s)…

A: We have given a function and finding point for local minimum value

Q: Use integration to find the area between the functions y = x² and y = 3x + 4. Show your work. -4 YA…

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Q: Let C be the curve y = 12 11 10 9 8 7 6 5 4 15 x³ 1 + 4 3x 25 Find the arc length of C shown above.…

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Q: Let C be the curve y = 12 11 10 9 8 7 6 10 T 15 4 1 + for 0.6 3.7. 3x 25 3 Find the arc length of C…

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Q: Juan Dela Cruz wants to deposit ₱5,000 every quarter at 16% compounded quarterly for 5 years. How…

A: We have to find out solution

Q: Question 11 If sin(0) = 7 and is in the 3rd quadrant, find cos(0) cos(0) = Enter your answer as a…

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Q: calculate the derivative below using the definition of derivative. f(x)=e^[cos(x)]  a = pi/2

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Q: The Taylor series for f(x) = x³ at 4 is Σ cn(x − 4)". n=0 Find the first few coefficients. CO C1 =…

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Q: Given the values of f(x), g(x), f'(x) and g'(x) in the table, answer the following questions. x f(x)…

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Q: Sketch a graph of the function f(x) = 3 cos 6 5 4 3 2 1 -8п -7п -бп -5п -4п -3л -2л -π -1 -2 -3 -4…

A: This question is based on graphing a function from its principal function.

Q: (a) Find the integral of 6.x8 √21° +7 dx. **IDENTIA YAMIMATIO

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Q: a. Find an equation for the secant line through the points where x has the given values. p. Find an…

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Q: Let a = -27 +53 + 4k. Find a.

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Q: 5. Solve d²y dy dx² dx +2 + 5y = sin 2x, given that y(0)=3, y'(0)=0.

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Q: Find the general solution of the differential equation. dy dt 8 ,t20 The general solution is y=.

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Q: Consider the triple integral of f(x,y,z)=(z²)(x²+y²+z²)¹/² over the solid region S where z is…

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Q: Prove the statement using the €, & definition of lim(x² + 2x - 7) = 1. →2

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Q: As the selling price of a product increases, demand decreases. Fewer people will buy a pro s more…

A: NOTE: Refresh your page if you can't see any equations. . the demand function is  and the revenue…

Q: Given the function of f(x) = 2x² - 10x +9 on the interval [-2, 0], find a point c between -2 and 0…

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Q: Question 2 Given the equation -5x² + 30x - 5y2 - 10y - 5z2 - 90z – 5z² 90z = 210 a) Show that the…

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Q: 25. Maximum revenue. A deli sells 640 sandwiches per day at a price of $8 each. (A) A market survey…

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Q: If 4x² - y² = 64, show that ds² = 1/2 (15x² (5x² - 16) dx².

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Q: (,1) Convert (5,5) to rectangular coordinates: (solve) Option 2 Option 3 (3√5,2) Option 4 Option 1…

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Q: Increasing global temperatures raise sea levels by thermal expansion and the melting of polar ice.…

A: Given L(x)=0.02x3-0.07x2+8x where x is the number of decades since 2000.

Q: A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

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Q: use a graphing utility to graph f(x)= -0.2x^3 - 0.5x^2 + 4x -4 on the interval [-6,4] and…

A: The given function fx=-0.2x3-0.5x2+4x-4 on the interval -6,4

Q: Sketch the graph of a function that satisfies the following conditions

A: Given

Q: f(x) = e6x + e−x find the locacl minimum value of f

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Q: Given the points A(7, -2, -9 ) and B( 7, −2, 2 ). Question 3 a) [:] Write parametric and symmetric…

A: We have to find the equation of line and intersection of line and plane.

Q: The number of people in a town of 65,000 who have heard an important news bulletin within t hours of…

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Q: Let C be the curve y = 12 11 10 9 8 7 6 5 4 15 x³ 1 + 4 3x 25 Find the arc length of C shown above.…

A: y= x3/4 +1/3x , 0.6&lt;=x&lt;=3.7  Find arc length First solve √(1+y'2) .

Q: Evaluate the improper integral or state that it diverges. ∞0 S 125 dx 3 Select the correct choice…

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