Use Green's Theorem to calculate (4z? - 3yz)dr + (3zy + Vy? + 6)dy, where Cis the circle (r – 1)2 + (y - 2)2 = 4. Consider counterclockwise.

Q: Prove that the following statement is true for all positive integers. 1 1 1 + + 4 8 1 2" – 1 + 2n Pn...

A: Given; Pn : 1/2 + 1/4 +1/8 +...+1/2n =(2n -1)/2n

Q: The following diagram shows a sketch of a curve with equation y = f(x). The points A(-3, 0), B(0, 0)...

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Q: 1. Consider the relation R1: R2 - R such that (r1, y1)R1 (x2, y2) if and only if both points are on ...

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Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

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Q: sin 3x Given: -dx_what is the appropriate formula to find the integral?- cos2(3x) (4-3 sec 3x) A du ...

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

A: First we find radius of convergence. Then find interval of convergence. 

Q: Determine if -1 CSC if 0 1 is continuous or not at r = and 1. If it is discontinuous, identify the ...

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Q: Use Pascal's triangle to expand (2x+3)6 Use Pascal's triangle to find the first three terms only of ...

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Q: B. Determine the function which coincides with f(x) for all values with the exception x = 5. (x² - 2...

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Q: Question 2 du where u= {(x) and for some constant, k. Compute /\2). The integral reduces to e + 1 A ...

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Q: Use the binomial series to find the Maclaurin series for the function. 4 f(x) = V1 + x 1 f(x) = 1 +-...

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Q: Evaluate the integral 4x4- 12x2 +7 xdx.

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Q: dy 2. V16 + y²

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Q: Use the above theorem to find the sum of each series. NOTE: Write your answer in the form of a reduc...

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Q: Solve the components of the given equation of conic sections and sketch the graph а. х — -y2 +1 b. x...

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

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Q: 2. Find the equation of the tangent line to the curve at the given point by eliminating the paramete...

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

A: Given sequence is GP. and ntg term of gp is an =arn-1

Q: The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventua...

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

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Q: cot (2x) -dx. Evaluate the integral V cot2 (2x)- 15 csc (2x) CSC A --Arcsec 8 +C 4

A: I=∫ cot(2x)cot2(2x)-15I =-∫ -cot(2x)csc(2x)csc(2x)csc2(2x)-1-15 dxcsc(2x)=u-2 cot(2x)csc(2x) dx = du...

Q: Some integrals that can be evaluated by hand cannot be evaluated by all computer algebra systems. Ev...

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Q: Calculate F. dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the plane...

A: We have to find double integral of F. ds

Q: Determine whether the series converges, and if so find its sum. 4k+2 7k-1 k=1

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Q: Question 1 dx The integral can be re-written as A lim (-1+2 y 1-m m - 0 B none of the choices lim (2...

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Q: Find the 30th derivative of y = cos(2x). f(30)(x) =

A: Take the derivative multi times and observe the pattern then write the required answer. 

Q: sin 3x Given: -dx What is the appropriate formula to find the integral? cos? (3x) (4-3 sec 3x) du (A...

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Q: Let F = %3D So Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the ...

A: Here, the given function is F=xy,5z,4y To use Stroke's theorem: ∫CF·dr=∫∫S∇×F·N^ dA And, ∇×F=ijk∂∂x∂...

Q: B. Prove that the given equation is a solution to the given DE: 5. x= 2t + C; y = Ct + 3 ; 2(y')2-xy...

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Q: Determine whether the given series converges or diverge E3n°4-n n=1

A: solution:-∑n=1∞3n34-n an=3n34-n an+1=3n+134-n+1 Ratio testL=limn→∞an+1an=limn→∞3n+134-n+1 3n34-n =li...

Q: I. Determine the derivative of the ff. exponential functions 1. y = 8 e -4x 2. y = 15 e 7x + 3 3. y ...

A: As per our company guidelines we can answer only three subparts question at a time, but if you need ...

Q: 7. What is dx (x six(x)?

A: Since you have asked multiple questions in a single request we would be answering only the first (7t...

Q: Consider -dx. Using u-substitution and transformation of integrand, then the power formula applies; ...

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Q: Question 5 5 Given: dx. Using u-substitution and transformation of integrand, what is u and du? 3/x ...

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Q: If the solution to e2x sec2(e2x+1)dx is equal to ktan (e2x+1) + C, find the exact value of k. 1 (A) ...

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Q: Write the given series: 2+4+6+8+10 in sigma notation.

A: Given problem:- Write the given series: 2+4+6+8+10 in sigma notation.

Q: Find the solution of the following Differential Equations 2) (xdy – ydx)/x² = 4) 2.x In(y)dx+ yx'dy ...

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Q: 3) A businessman ventures to put up a digital printing shop which caters to printing of t-shirts for...

A: Let the number of t-shirts that will obtain maximum gross return is = 50+x. In this case x t-shirts ...

Q: 3) A businessman ventures to put up a digital printing shop which caters to printing of t-shirts for...

A: Let the number of t-shirts that will obtain maximum gross return is = 50+x. In this case x t-shirts ...

Q: Solve the following, glving the solutlons In the form ptqvr 6x +15 Rationalise the demoninator of th...

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Q: Determine whether the given series converges or diverges n2 Σ 2n In n n=1

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Q: The diagram below shows points P, Q and R. The coordinates of the points are given by P (2), Q(5, 6)...

A: Distance between the points P(x1,y1) and Q(x2,y2) , D = (x2-x1)2+(y2-y1)2 .

Q: x² - 36 lim X6 x+6 (a) Vx+11-4 lim (b) x-5 (c) lim- x2 2-x x +6x+9 lim (d) r+3

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Q: 2) y'+2xy = 0

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Q: 8-2х (f) lim- нх* — х—12

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Q: 2) An agriculturist wanted to plant seven different organic crops in a small field. To properly stud...

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Q: 2) Find the tangent to the curve y 2 tan at x 1.

A: A detailed solution is given below.

Q: f(x)= (x-2)/(x^2-x+1)^2the intervals on which f is increasing or decreasing (d.) the intervals on wh...

A: Given functionfx=x-2x2-x+12We will answer sub-part c, d and e(c) the intervals on which f is increas...

Q: Use the limit comparison test to determine whether the series converges 8. 7h +5 im The series conve...

A: The given series, ∑k=1∞87k+5  

Q: dx The integral can be re-written as. VI- A lim (-2+ V1- m) m-- 00 B none of the choices lim (2-2 V1...

A: ∫-∞0 dx1-x