Use Green's Theorem to evaluate F. dr, where F(x, y) = (y - cos y, x sin y) and C is the circle (x - 3)² + (y + 4)² = 4 oriented clockwise. (Check the orientation of the curve before applying the theorem.)

Q: eſt 2 du given that * f(z) dx = 12 f(4Tan¹(u)) 1+u² Evaluate

A: Hint :  This problem is application method of substitution in definite integral. If you have not…

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A: Given query is to find the population after 4 days.

Q: Rewrite the following series using the E-notation. 1 1 1 1 1 + + + + + + 10 17 26 37 12

A: Solving

Q: 9) Evaluate the following indefinite integrals a. [(5x¹ + x² + x) dx b. 9x²(x³ +5)*dx c. S7 C. dx…

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Q: Find the arc length L of the graph of r(t). L: = r(t) = 10 cos(t)i + 10 sin(t)j + tk, 0≤t≤ 2π

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Q: ∫12v (7+6v2)9 dv Evaluate the following integral using substitution rule or integration by…

A:

Q: Find the area of the shaded region. = √cos 20 9 cos X r

A: Area = integration of 1/2 (r2^2 - r1^2) d(theta)

Q: 1. Find the area of the region enclosed by the given curves. a) y - x² = 2x and x + 4 = y b) x = y¹,…

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Q: Use L’Hospital’s Rule to evaluate the given limit.

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Q: face integral over t xk, portion of t n the octant x, y, z ing normal

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Q: dx x√√x4 - 4 S

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Q: Consider a triangle ABC like the one below. Suppose that A = 65°, B=55°, and c=40. (The figure is…

A:

Q: s dx x+√2x+1

A: Let  2x+1=u ⇒dudx=12x+1 ⇒dx=2x+1du also x=u2-12  ∫dxx+2x+1=2∫uu2+2u-1du…

Q: Find the arc length L of the graph of r(t). r(t) = t3 i+t p j+126t2 k, 3≤t≤6

A: r(t)=t3 i +t j+126t2 kdxdt=3t2dydt=1dzdt=252 t3≤t≤6

Q: The concentration of a certain drug in the bloodstream t minutes after swallowing a pill containing…

A:

Q: Write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 9x²,…

A: Given query is to find the equation of the parabola.

Q: 1. If z = f(x, y) has continuous second-order partial derivatives and x = r cos 0, y = r sin 0,…

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Q: Use Stokes' Theorem to evaluate for F. dr. F(x, y, z) = 5xyi + 5yzj + 5zxk C where is the triangle…

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Q: Determine whether each of the following series converges. (Make sure to state which test you are…

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Q: 14) Find the mean value of the function y = 4 - x² on the interval [-1,2].

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Q: A 40-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 7…

A: Find the rate of the top of ladder sliding down.

Q: ∫(2 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

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Q: ompute the surface integral over the given ented surface: = y'i + 7j - xk, portion of the plane - 1…

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Q: Plot the curve c(t)=(2t−1,²+3). Then find the length of the curve for 1<t≤2 to two decimal places.

A: Curve is ploted and length of curve is obtained.

Q: [2 2x³ (x² − 1)² – dx|

A:

Q: 1.57 1 (1.5,2) (-0.7,02) (0.7,0.2) -1.5 -0.5 1 1.5 --0.5+ -1.5 Where does f have absolute minimums?…

A: Recall:  In graph, y-coordinate at the lowest and highest points are called the absolute minimum and…

Q: Find the following using the table below. X 12 3 4 f(x) 3 1 4 2 f'(x) 4 1 2 g(x) 2 4 1 g'(x) 2 3 4 1…

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Q: Strontium-90 is a radioactive material that decays according to the function A(t) = A e scientist…

A: This question can be solved using the concept of exponential growth and decay.

Q: Determine whether the statement is true or false. If C is a smooth curve in the xy-plane and f(x, y)…

A: Given

Q: (3x+4)2dx Evaluate indefinite anti-differentiation

A: The given integral is (3x+4)2.

Q: 2π сos20 Using complex variable techniques evaluate the real integral: 2 dᎾ . 4-3cos0 Classify the…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for…

Q: Let (3, 4) be a point on the terminal Find the exact values of cos 0, sec 0, cos ( = 0 sec 0 = 0 cot…

A:

Q: The curve is given in polar coordinates by r = e³0. Let A be the point on the curve corresponding to…

A:

Q: Let f(x)= x+1 1³ - 2x² + 1

A: Solving the problem by finding the fraction from the expression.

Q: Looking up, Jim sees two hot air balloons in the sky as shown. He determines that the lower hot air…

A: Follow the procedure given below.

Q: 1) Find the average value of the function f define by f(x)=√√√49-x²³² On the interval [0, 7] 2) Find…

A: We can use the equation to find average value of a function in an interval.

Q: ∫cos(7t) dt Evaluate indefinite anti-differentiation

A: LetI=∫cos7tdtPut 7t=uDifferentiate on both side7dt=dudt=du7ThereforeI=∫cosu17duTake the constant…

Q: A function is said to have a horizontal asymptote if either the limit at infinity exists of the…

A: limx→∞ x2+8x3-11x=limx→∞ 1xx2+8x1x(3-11x)=limx→∞ x2+8xx23x-11

Q: Scos2x (2 cos2x-1) dx

A:

Q: The half-life of radium is 1690 years. If 80 grams are present now, how much will be present in 360…

A: Given query is to find the amount remaining after 360 years.

Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

A: Given,            fx=5x2-20x+ with domain 0,3

Q: Estimate the integral right-hand sum with n = 3 subdivisions. Left-hand sum Right-hand sum - [₁2 2…

A: To solve the following problem

Q: Consider the following. y 20 15 10 f(x) = 25 (5, 25) g(x)=x² 5 -4 -2 2 4 6 Q (a) Form the integral…

A: Given query is the area of the shaded region.

Q: The decay rate for a radioactive isotope

A:

Q: Evaluate Ic (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) X

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Q: Find the extreme values of on [-2,2]. f(x) = ret, x < 0 2x³9x² - 12x, x ≥ 0

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

Q: Find the exact area under the graph of f(x) = = and x = 2. Area = 1 x+1 between r=0

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Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j + tk; t = T() 6 37 0, √/3 X N…

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Q: 1. Determine the following using the graph off provided below. If the value is infinite, specify oo…

A: x→a+ means; x approaching to value a from the right side.Equation of straight line:(-7, 3) and  (1,…

Q: Solve the differential equation de 4d³-13 +6y=0 dy dx

A: To solve the given equation.