If the power of the cosine is odd and positive Convert the remaining factors into cosines Convert the remaining factors into sines Save a cosine factor Save a sine factor

Q: Calculate the volume of the solid obtained by rotating the area bounded by f(x) the x(x + 1) X-axis,...

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Q: Question 1 Suppose the infinite series an is divergent. Then for any real number c, the series can i...

A: We have to choose correct option

Q: Find the equation of the tangent plane to the surface z = e17 In(1y) at the point (-3, 1,0). Note: Y...

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Q: 6. Use the sum and difference identities to simplify the expression. '5T COS 12

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Q: You want to build a 1100 square foot rectangular infinity pool. Three of the sides will have regular...

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Q: С. 1 Evaluate the following limits x2 +6x+5 1) lim x-5 x²+2x-15 x(х-5)-24 2) lim x→8 x2-8x (2+x)3-8 ...

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Q: tf(r.,2) 4ry t and u is the unit vector in the direction of (4, 2,-5), tmen the drectional denvative...

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Q: +00 El-1)nInn- n=2 n2

A: The given series,        ∑n=2+∞-1nln nn2

Q: You want to build a 1100 square foot rectangular infinity pool. Three of the sides will have regular...

A: Topic:- algebra

Q: 12 + csc 0 [sin 0 + csc 0]d0

A: Given I=∫12+cscθ(sinθ+cscθdθ To evaluate the integral I

Q: Determine whether the improper integral diverges or converges. 1 dx e6x + e-6x converges O diverges ...

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Q: Given that x2 -y² = 9, then dy/dx = %3D

A: Topic = Derivative

Q: Q9/ Find the centroid of the region enclosed by the cardioid r = 1 + cos 0.

A: 5/6 centroid

Q: For the function, find any horizontal and vertical asymptotes x2 + 16 y = horizontal asymptotes vert...

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Q: 8. Use the image below to answer the following. Show your work, but you may use technology to calcul...

A: The centroid of a region R is given by x, y=MyM, MxM, where we have M=∬RdA; My=∬Rx dA and Mx=∬Ry dA ...

Q: +00 (-1)" n! n=1 O convergent O divergent

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Q: A particle moves along the x-axis so that at time t >0 its position is given by x (t) =t² – 10t + 10...

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Q: interal [ozd Upper Rucimann Suns f(akx²tx »- Caletete the Lowe intertal [0,2] Upper Riemann Snas f(x...

A: Solution is written in below steps.

Q: 2 sin? x - 7sinx + 3 = 0

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Q: Find the least amount of different numbers to pick from positive integers that are at most 100 to gu...

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Q: cotx da cos I da sin r 3.

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Q: Question Given the triangle below, find tan(0). Enter the answer as a fraction. 53 28 45

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Q: Two sides of a triangle have lengths 10 m and 15 m. The angle between them is increasing at a rate o...

A: rate of change in side

Q: Solve the initial-value problem by using integrating factors. xy' = y + 4x ln(x), y(1) = 3

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Q: dy + 4y = 8 dy d. x- dx = (x – y)² %3D a. dr dy e. da dy + 4y = x? %3D b. = V1+x2 %3D dx dy dy c. dr...

A: This can be solved as follows:

Q: Solve this differential equation: 0.07y(200 – y) y(t) =

A: Given: Now,               y' =0.07y200-y⇒dy0.07y200-y=dx⇒dy-0.07yy-200=dx⇒114y+-114y-200dy=dx⇒114y-...

Q: For the function, find any horizontal and vertical asymptotes. (Enter your answers as a comma-separa...

A: To find out the vertical and horizontal asymptote. 

Q: The half-life of cesium-137 is 30 years. Suppose we have a 130 mg sample. (a) Find the mass (in mg) ...

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Q: Af(x)

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Q: 4.) Find y': Given:y = x²(3 cosh x - 1) 5.) Find y': Given: y = log, csc h (6x³)

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Q: I Eliminate the arbitrary constants -2x 2X Y = C,e cos 2× + Ge sin 3X

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Q: 77. The rate at which water leaks from a tank, in gallons per hour, is modeled by R, a differentiabl...

A: Consider a function y = f(x) .Then f '( x0) is the rate of change of y with respect to x at the poin...

Q: (-1)"+l2nx" Determine the interval of convergence of2. n² +3 n=1

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Q: Evaluate the following. x2 - x 1 dx J1+3x2 – 2r3 CO 2 dx 1+2 sin a x2 +2 dx r+1 2)

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Q: VI. Give the Maclaurin series expansion of f(r) = In(3 – 2r). Determine its interval of convergence....

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Q: If f(x) 5æ - 2x 2x3 find f'(x) x4

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Q: 4. The goal of this problem is to show that x² Q(x) = 1+x + is the quadratic approximation to f(x) =...

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Q: Is the differential equation linear? y' = y + ey

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Q: 3. Let p = 31. Evaluate L3(24).

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Q: PERFORMANCE TASK Carl and his friend James are having trouble using the different methods for findin...

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Q: 3. Determine the set of points at which the function is continuous. (a) F(x, y) = V1+x – y (b) G(x,y...

A: To find the sets where the function is continous. Note that, the function is continuous on a set whe...

Q: Find the average value of the function ( x) in the interval [- T, n]. f(x) = sin xcos'x а. п b.0 C. ...

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Q: 4. f(x) = a = 0 x2-4x %3D x2+4x x?-3,xミ-1 5. f(x) = {x- 1, x>-1 こa=-1 %3D

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Q: MODULE IN BASIC CALCULUS IV. Exercises 1. Determine the general antiderivatives of the following fun...

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Q: Consider vector u. Find the angle 0 E [0, 27) that vector u makes with the positive direction of the...

A: Given:-u=92i-92jux=92uy=-92θ∈[0, 2π)

Q: 2. Consider the series E (In(2n + 1) – In(2n – 1)). n=1 (a) Let a, = In(2n + 1) – In(2n – 1). Does {...

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Q: 10- y 8- 2-

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Q: Consider the following. 1+ e2x + 1 = 15 (a) Find the exact solution of the exponential equation in t...

A: Topic = Algebra

Q: Find ag and an for the following geometric sequence. a4 = 8, r= - 2 Find a, for the geometric sequen...

A: The objective of the question is determine the a5 for the geometric sequence.

Q: he directional de -) = 3x?y -4xy 3x², 2. %3D ne giu divection gie

A: