1.) Evaluate: S sin*xcosxdx 2.) Evaluate: Sx³Inxdx 3.) Evaluate: Sx3*dx

Q: 3) Find the sum of the first 12 terms of the geometric sequence-3,-6,-12,-24,..

A: We can solve as follows

Q: Write the sum using sigma notation: 9+ 13 + 17 + 21 + ...+ 57 = B, where n=1 A = B =

A: Topic:- sequence and series

Q: Use the substitution method to find all solutions of the system of equations. S2x + y = 5 x + 2y = 1

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Q: Simplify the following expression. dt dx 2+1 dt .2 dx t +1 0.

A: In the given problem first we integrate the given integrand and  then differentiate the integral .

Q: Use the Definition to find an expression for the area under the graph of f as a limit. Do not…

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Q: 8. Determine by the ratio test if 2n=1 (2n)! converges or diverges.

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Q: A roctangular tonk uith a cauaro boco and a volumo of 2.016 e3 dimoncions of tho tank that hac 1o…

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Q: dr J. (z+1)?

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Q: A region in the xy- plane has a z-output given by the equation z = In(x?) + 2xy - e*y. Determine the…

A: the volume between the x-y plane and below the z-axis is given by V=∫x=∫y=∫z=dzdydx According to the…

Q: Ing light is located 10 feet from a wall. The light completes one rotation every 3 seconds. Find the…

A: From the given data: Here, the complete 2π rotation is done in 3 seconds.  So, dθdt=2π3 rad/sec

Q: / (22* + 3,/5 +) Calculate the indefinite integral: dz

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Q: the area under the graph of the function over the interval given. 25) y = 2x +7; [1, 5] A) 18 B) 52…

A: Given query is to find the area under the graph.

Q: Q2) Find the volume of the solid generated by revolving the "tri- angular" region bounded by the…

A: Washer method: To find the volume enclosed between two functions, the washer method is applied. We…

Q: he volume, V, of a sphere in terms of its radius, r, is given by V (r) = Tr3. Express r as a…

A: Topic:- function

Q: Given the curve y = x´ and the lines y = 0 and y = 2 – x wwww Find the ordinate of the centroid Y חו…

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Q: 3. A curve has equation y = Find the x-coordinates of the stationary points of the curve in the tan…

A: To solve the following problem

Q: Evaluate the following integral. x² dx X +6 x2 dx X +6 II

A: topic - indefinite integral

Q: 3) Find the sum of the first 12 terms of the geometric sequence -3,-6,-12, -24, ..

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Q: solve

A: We will solve the problems.

Q: ou can compare using the Limit Comparison Test. Then deter 00 1 1 Σ C. and D. 1 n2 n3 n=1 n3/2 n=1…

A: We have to match according to the given information

Q: ssume that the two points (x1.y1) and (X2.Y2) lie on the graph of the straight line y = mx +b. Use…

A: here, i am providing my handwritten solution

Q: Question 1 The position vector of a particle is r(t). Find the requested vector. The acceleration at…

A: Topic  = Derivative

Q: dA when T = 5. dt dr Let A be the area of a circle with radius r. If dt 2, find %3D

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Q: Dr. Barrett wants to purchase a new piece of equipment for his practice. The eauipment can be…

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Q: 1 3 4 5 6 7 Equation an 9 14 20 27 1 3 12 60 360 2520

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Q: Evaluate the surface integral. (x + y + z) ds, Sis the parallelogram with parametric equations x = u…

A: Solution: ∬(x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z…

Q: yA C(0, 1) B(1, 1) y = Vx R2 R3 y=x³ %3D A(1, 0) Referring to the figure above, find the volume…

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Q: Determine the, 5 a.) E [3xyi - 10] |=1

A: Sum

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

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Q: Listen Use the Ratio Test to determine if the series converges or diverges. (2n) Σ 3n(nl)2 n=1…

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Q: tind ds 3\nx when

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1 18 6 The sum is (Type an integer or a simplified fraction.) 1/2 1/6

A: Topic:- sequence and series

Q: 1. It is a list, or an array of numbers arranged in a definite order. a. ordering C. arrangements d.…

A: Ans 1.       A sequence is a set of numbers  arranged in a definite order. and the numbers in the…

Q: From Rogawski ET 2e section 8.4, exercise 1. Calculate the Taylor polynomials T2(x) and T3(x)…

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Q: Describe the given region in polar form a.) b.), 1 1 2/3

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Q: g integral. dx

A: Given query is to find the value of the integral.

Q: dy - cosec'x. cos x (i) By differentiating 6 show that if y = cot x then sinx' dr (ii) Show that x…

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Q: Find the inverse of the function on the given domain. f(z) = (x – 14)2. [14, 0) f-1 (2) =

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Q: A particle is moving with acceleration a(t) = 6t + 16. its position at time t = velocity at time t =…

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Q: 11. Solve the second-order differential equation y" – y' – 2y = 20 cos x using the method of…

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Q: The future value at 5.25% interest, compounded continuously for 7 years, of the continuous income…

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Q: dr 15. (4 – 2²)3/2

A: Topic = Integration

Q: Find all local extreme values of f(1) = 2 + 8x - 30. %3D | The FIRST local extreme value, moving…

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Q: Use a change of variables to find the indefinite integral. Check your work by differentiation. 1…

A: To integrate.

Q: %24 #3 %3D (Copy) Questic Find all vectors u that satisfy the equation (1,1,1) xu = (-2,- 1,3).…

A: The solution is given below

Q: 3. Find two elevation angles that will enable a shell, fired from ground level with a muzzle speed…

A: Solution: here we use the range formula

Q: Use the table of frequently used Taylor series to find the sum of the series. - 3+ 6x - 9x + 12x -…

A: Solution

Q: Divide 4x^4-3x+11x^2-x-1 by (4x+1)

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Q: Find the area of the parallelogram that has two adjacent sides u = -2i + 4k and v =i +2] +k Axn pu…

A: We will find the cross product and area.

Q: A mountain climber is about to haul up a 70-m length of hanging rope. How much work will it take if…

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