Exercise: Show that x vzdA = Qdx2 Therefore, we have x vidA+ V x VzdA = |_ Pdx1 + Qdra = ▼ × vdA = · dr D

Q: sin 4zdz J 16+ sin ª 2= 4.

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A: Find your answer below 

Q: 5. 3x² + x -1 x+2 A 3x2 + 5x + 9 In I x + 21+C 2. 3x2 - 5x + 9 In I x + 21+ C 2. B 3x2 + 5x + 9. + C...

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Q: +00 n! と+1 n=1

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Q: 4 81-72sin²0+16sin*6 do S sin 20 de 1–2cos²0+cos40

A: Let I=∫sin2θ81-72sin2θ+16sin4θ1-2cos2θ+cos4θ4dθI=∫sin2θ92-2*9*4sin2θ+4sin2θ21-2*1*cos2θ+cos4θ4dθI=∫s...

Q: c. Evaluate the integral. 4 c3 4. S S(x² + 3xy²)dxdy

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Q: 3. x In x A In С п IInxI + С - + C Inx B D In I In xI + C Inx

A: ∫πx ln xdx

Q: () = 2 sec(a O conon1 O pton 2

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Q: 1. Given the function f(x, y) = x² /ÿ. (a) Find the local linear approximation of f at the point (3,...

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Q: If a tank holds 4500 gallons of water, which drains from the bottom of the tank in 50 minutes, then ...

A:  Given:         V=45001-150t2 0≤t≤50     the rate at which water is draining is given by      dVdt=d...

Q: Find the general term of the sequence, starting with n = 1, determine whether the sequence converges...

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Q: 5) Suppose the function C(1), where trepresents the number of months from January 1, 2020, approxima...

A: Given, C(t)  represents the energy cost to a manufacturing company, where t is the number of months ...

Q: A graphing calculator is recommended. A particle moves according to a law of motion s = f(t), t 2 0,...

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Q: A ball is thrown downward with a speed of 14 ft/s from the top of a 196-foot-tall building. After t ...

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Q: Evaluate the slope of the function: a. f(x) =x^2 + x - 2                              at x = -1.5 b...

A: Here we have to find the slope of the given different functions.  

Q: Determine the sum of the following series. NOTE: Enter the exact, simplified answer as improper frac...

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Q: Use the differencean+1 – an to show that the given sequence {a, } is strictly increasing or strictly...

A: Difference = an+1 - an= (n+1)9(n+1)-8 - n9n -8=(n+1) 9n+9-8-n9n-8=n+19n+1-n9n-8=(9n-8)(n+1)-n(9n+1)(...

Q: Use the binomial series to find the Maclaurin series for the function. f(x) = V1 + x f(x) = 1 +x+ 3....

A: Find your answer below 

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an imprope...

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Q: Example 6 If ð = (3, 2), b =(5, –1), ĉ = (-4, 2) find (a) 2a + b – 3c (b) 3a + 26 – 7.

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Q: sin &x -& sec x) dx

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Q: derivative

A: We will find the derivative. 

Q: Perimeter & Area Puzzler #10 Read the problem and solve. Show your work here: At the zoo a new habit...

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Q: Evaluate the slope of the function: (Please solve using limits)  f(x) = 1 - x^3                    ...

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Q: 6х2-17х+25 10. S: (х-1)(х-2)(х-3)

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Q: れcot1 (3x) e dx Evaluate yuis

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Q: Given f(x) = 2 /x + 2, find f'(x) using the limit definition of the derivative. f'(x)=

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Q: Use any method to determine whether the series converge. 5 (a) E k=l Vk +1 This series cos () (b) > ...

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Q: 3.44 Given that F= x'ya, – ya,, find (a) $¸F·d1, where L is shown in Figure 3.30. (b) Ss(V × F) · dS...

A: The given problem is solved below in detail.

Q: 2x3+3x dx x4+3x² In lx* + 3x²1 + C 1 + C In(x4+3x²) C В 1 D 1 1 - In Ix* + 3x²1 + C + C 2 In(x4+3x²)...

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Q: Suppose that a population of bacteria triples every hour and starts with 200 bacteria. Find an expre...

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Q: (3y- 2 )cy y´+2y+17

A: We have to evaluate value of given indefinite Integration.

Q: de 962 +120 + 9

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Q: xy+yz b) lim (xy2)-(0.0.0) x+y2+2

A: To find the limit: L=lim(x,y,z)→(0,0,0)xy+yzx2+y2+z2

Q: Determine whether the alternating series converges. 2(- 1)*+1 k+ 1 2k + 1 k=1 O The series diverges....

A: Alternating series test: Suppose that we have a series ∑ an and either  an=(-1)nbn  or an=(-1)n+1bn ...

Q: A function f has a removable discontinuity at x = c if limf(x) exists by f is not continuous at x = ...

A: Here, the given function is: f(x)=x-2|x|-2 So, function is not defined at x=2,-2

Q: Suppose that the revenue from selling x radios is R(x) = 75x - dollars. Use the 10 function R' (x) t...

A: Here, the given revenue function is: R(x)=75x-x210⇒R'(x)=75(1)-2x10=75-x5

Q: The table shows values of a force function f(æ) where a is measured in meters and f(x) in newtons. U...

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Q: Find the solution of the following Differential Equations

A: We are asked to find the solution of the differential equation

Q: 4. Complete each statement: a) The points of inflection are found by solving the to zero. equal b) T...

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Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an imprope...

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Q: 1 1 Зп — 1 3n + 2 n=1

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Q: 1 dx O (1+ x)1/4 1.

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Q: Convert this identity to one using sine term(s) only. 1 - 2 cos2r = 2sin²r - 1 -1 - sin²r 1 - 2sin...

A: This question is based on conversion of Cos2r = 1 - Sin2r

Q: Set up the definite integral required to find the area of the region between the graph of y = 12 – x...

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Q: +o0 2" +1 3" +n n=1

A: Let's find. 

Q: sc 2x - cot 2x = 0 1 sec

A: We have csc2x-cot2x=?

Q: Given h(x, y, z) = 4Vx+ ln (y² + z²+1). (a) Find the directional derivative of h at the point (1,0, ...

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Q: x³ + 5 dx x4 – x3 + x²

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 7 Pa(x) =

A: Taylor series of function fx at a is defined as:       fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…=ln7+d...