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Q: Use cylindrical coordinates to evaluate the integral below. F √x² + y²dv, where E is the region that…

A: We can solve this as follows:

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

A: We need to find maxima and minima.

Q: Verify the identity. cot tcsc t= 2 csct-1 cos t Which of the following three statements establishes…

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Q: An estimate of ³₁x¹dx using Simpson's rule with n = 4 gives a. b. C. d. 242 5 244 5 148 3 152 3

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Q: 59 Find the reference angle for the angle 12π Since the given angle is greater than 27 = 6 we find a…

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Q: 5. S (2x+1) dx (x+4)*(x-3)6

A: Given - ∫(2x+1)(x+4)6(x-3)6dxthen we know that -…

Q: dy 18. x dx (1 + x)y = xy²

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Q: Find the equation of the tangent line to y=−6/x^2 at x=−2. Write your answer in slope-intercept…

A: The equation of the curve is y = -6x2 To evaluate: The equation of the tangent line to the given…

Q: A manufacturer has determined that the total cost C of operating a factory is C = 2x² + 60x + 200,…

A: Firstly we have to solve for average cost per unit as given in the question.  Then apply…

Q: 1. Differentiate the following and for each state whether you have used the product rule and/or the…

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Q: 00 Several terms of a sequence (an) n=1 are given. a. Find the next two terms of the sequence. b.…

A: NOTE: Refresh your page if you can't see any equations. . the given sequence is  the first term is…

Q: Given that the DE y" (t)-6y' (t) + 6y(t) = 2e6t has a solution of the form Ce6t determine the value…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of sin(x) (cos(t²) + t)dt…

A: Given that , hx=∫-1sinxcost2+tdt h'x=?

Q: D 5 yo

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Q: y 200 150- (-3.75,93.75) 1000

A: increasing interval where slope increading

Q: Evaluate the indefinite integral sin² t cos³ tdt = + C

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Q: Find the area of the region enclosed by y = 3.25x and x = 3 - y². 2 Use horizontal strips to find…

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Q: Q1: lim Q2: lim (x-1)(x-2) x+1 x-001+stnx Q3: f(x) = x²-16 đêm 5244 A) 3 (A) B) 00 (B) 00 18 (C)-8…

A: We need to find limit.

Q: 14. 2y dx + x(x² In y − 1) dy = 0. -

A: To find the solution of the given differential equation.

Q: slope y-intercept Draw the graph. ● No Solution y=- — x Help -10 m = (x, y) = 88 x -3 -2 -1 10 0 8 7…

A: Graph

Q: Solve the differential equation dy da - y²+7xy+16x² x² a. x + y = O b. x Y = ; when x = 1, y = 1 5…

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Q: 150 5 -4 -2 100 50 -50 -100 -150 200! 2 4 6 8 Xx

A: We know that, The highest point the graph ever reaches is the absolute maximum. The lowest point the…

Q: 1. The position of a particle moving in the ry plane at time t units is given by the vector equation…

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Q: 3 3 3 2 (49) (+91 i- -74+ i n n n integral, that is provide a, b and f(x) in the expression f(x)dx.…

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Q: 17. tan (cos x)

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Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

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Q: [1/3 Points] f(x) = DETAILS PREVIOUS ANSWERS Find an expression for the function whose graph is the…

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Q: b) y = (e² + √cos x) c) y = |l−tanx 3x³

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Q: Write the expression in power form ax for numbers a and b. 3 8 8x²

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Q: 6) Evaluate 0.8 1 0 dx 4x² +4

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Q: 4.y=log10 (x4 + 3x² + 1) 5.y = log5 √x² +1 1-x² 6.y-log10 |2–5x3

A: Given 4. y=log10x4+3x2+1 5. y=log5x2+1 6. y=log101-x22-5x3         Derivative of the log functions…

Q: (b) Find a particular solution for each of the given differential equations (i) y" - 6y +9y = e² - 5…

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Q: What is the integrating factor of the differential equation (5xy + 4y² + 1) dx + (x² + 2xy) dy = 0?…

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Q: Evaluate the integral: J22 SVA-2 01- [] π [] +C dydz 4-2² e² +²

A: double integration using polar form

Q: Find the indefinite integral and check your result by differentiation. (Use C for the constant of…

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Q: lve y' = 14xy – 2x, y(0) = 11 x) =

A: Topic:- application of integration

Q: The derivative of f(x) = tan- is: Select one: O a. O b. O C. O d. 1 x² cos² 1 -1 x² cos² 1 xcos² 1 F…

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Q: A particle is moving along the curve having the vector equation R(t) = ti+t²j+ tk. Find the vectors…

A: The given position vector is  Rt=t i + t2 j + t k.   The velocity vector is given by Vt=R't=i+2t j…

Q: Find the differential dy of the given function. (Use "dx" for dx.) 4 dy = y = 4√x + Submit Answer

A: To find differential dy for the given function.

Q: Find the limit, if it exists. lim X-- 12-1 xº-1

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Q: Find the difference quotient f(x+h)-f(x) for f(x) = x² - 4x. h

A: Here is the solution:

Q: Find the solution to the differential equation that passes through the origin. z(t) = dz dt = 6te42

A: dzdt=6te4z⇒e-4zdz=6tdtIntegrating both sides we get,⇒zt=-ln-12t2-c14

Q: Explain how the fundamental theorem of calculus relates integrals and derivatives. Formats T B T U…

A: Fundamental theorem of calculus relates integrals and derivatives.

Q: Given: R(t) = ti + t2j + t3k, find the curvature and the radius of curvature at any point.

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Q: 2 -1 4 3 N у -1 1 2 X

A: Graph of the function is given, we have to find its domain and range

Q: I. Find dy/dx of the following: 4. y=√1+In²x 7. y In- COS X √4-3x² 5. y = sin²(In x) 8. y In, x- 6.…

A: Topic - Derivative of a function Power rule: ddxxn=nxn-1ddxln(x)=1x

Q: Express a = the limit lim Σ(4(x*)² – 3(x* )³) Aï; over [6, 7] as an integral. n→∞ i=1 Provide a, b…

A: The given limit limn→∞∑i=1∞4xi*2-3xi*3∆xi over the interval 6,7

Q: Use the following information for Questions 4 and 5. f is a continuous function with a domain [-3,…

A: (5) Given that , fx=3,          -3≤x≤0-x+3,    0≤x≤6 -3,          6≤x≤9 and gx=∫-2xftdt Find gx in…

Q: An unknown radioactive element decays into non- radioactive substances. In 240 days the…

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Q: A stone is thrown straight up from the edge of a roof, 875 feet above the ground, at a speed of 14…

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