4. (i) Use the parametric equations of an ellipse, z = a cos (t) , y = bsin (t), 0 < t< 2r, to find the area that it encloses.

Q: The vertices of quadrilateral ABCD are given as A(0, 3, 5). B(3, – 1, 17), C(7, –3, 15), and D(4, 1,…

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Q: 1.) Evaluate: S(2 + y²)²dy

A: We have to find integral

Q: Solve the Indefinite Integral. S sin Vædz

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Q: Evaluate: J 1+sinx -dx

A: To evaluate the given integral.

Q: x = r° +1, y=r² -t a) Find dy/dx Show all your work.

A: x =f(t)dxdt=f'(t)   y=g(t)dydt=g'(t)Then,dydx=dydtdxdt =g'(t)f'(t)

Q: Following S sin(A) cos(B) dx = ; f sin(A + B) + sin(A – B), | what is the integral of f sin 5x cos…

A: We have to solve the following

Q: Consider the function below. f(t) = t + cost, -2n sts 2n (a) Find the interval of increase. (Enter…

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Q: 12. Evaluate the given integral, J x² sin x dx: A. - x2 cos x + 2x sin x + 2 cos x + c B. x2 cos x +…

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Q: Direction: Prove using the three conditions of continuity if the following function is continuous or…

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Q: t2 1- y? dy 6. dt dy ap 2ty? + 3t²y², y(1) = –1 5. r(0) = -2 y(0) = -2 7. dt dt

A: To find the solution of the given initial value problems.

Q: 23 — 4а2 + 8ах + 1 f(x) = 2? — 2х + 2

A: answer is in next step

Q: 8. A 5-gallon bucket is full of pure water. Suppose we begin dumping salt into the bucket at a rate…

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Q: Evaluate: dar x 3 - 40.471 2 40.187 2 40.748 - 20.748

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Q: 1(x) (х+1)* II

A: follow the procedure given below.

Q: clearly

A: We have to choose the correct option according to the given information

Q: Write the complex conjugate of the complex number. Then multiply the number by its complex…

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Q: Use the summation formulas to rewrite the expression without the summation notation. 2j + 7 n2 j = 1…

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Q: ntify the u , ress the final answer in its simplest form without onents. Thank You! du and other…

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Q: D(X) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

A: Here, the given functions are: D(x)=100x, S(x)=x

Q: Suppose a tour guide has a bus that holds a maximum of 100 people. Assume his profit (in dollars)…

A: P(n) = n(50 - 0.5n) - 100 P(n) = 50n - 0.5n2 - 100 Domain : [ 0,100 ] Now, P'(n) = 50 - n  To Find…

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Q: Find the distance from the point (3, 4, -1) to the plane lr 3y +2z = 5.

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Q: Find the derivative of the function. 4 f(x) x In(x) f'(x) %D

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Q: .2 x In x dx ; with (h = 0.1)

A: follow the procedure given below.

Q: .John can swim at 4km/h in still water. He wishes to swim across a river to a point directly…

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Q: Find the derivative of the function. -x + 1 r(x) : = |(7x – 4)(x – 8) -

A: Given that a function r(x) and we find derivatives of r'(x) .   We know that d(xn)/dx= nxn-1.…

Q: Simplify sec(arcsin ). no solution O (3V5)/5 O (2 V5)/5

A: Solving the problem by finding the value of the expression.

Q: Find the limit. 3x +3 lim 12x2 - 8 > Next Question

A: Given query is to find indicated limit.

Q: Find an equation of the plane through the three points given: P = (0,0, 5), Q = (-4, 2,2), R = (-1,…

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Q: should i write it with variables like x = 11, y = 11, z = 4? but it says exact number, no tolerance.…

A: The answer has exact form. You will not have to enter the variables.

Q: 4x 20. Write log2 assthe sum and/or difference of ² - 3x - 18 logarithms. Express powers as factors.

A: The given logarthim expression,       log24x3x2-3x-18

Q: Evaluate the following limit and show the complete solution

A: Given limit is in the form of 0/0

Q: 2. Let A = (1,0, 2) and B = (6, –2, 3). Solve for projĄB.

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Q: 3. Two sides of a triangle are 5 and 10 inches, respectively. The angle between them is increasing…

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Q: Find an equation equivalent to x²+ y² + 2z²+ 2z - 5 =0 in spherical coordinates.

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Q: x =r' +1, y =r -t = t a) Find dy/dx

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Q: 3920 - Sp22 5.4 A person's investment is expected to produce a continuous stream of revenue R of…

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Q: 5. S(x): x +4 4 4 b. x2 + 16 a. (x + 4)2

A: We will find out the derivative.

Q: What is a total weight of 7 basketball that weight 22 ounces each

A: Given each basketball weight is 22 ounces

Q: (a) Graph y = 200(0.45)0.7 for x= 0 to x= 10. (b) What is the initial value of this function (the…

A: We have to find the limiting value

Q: Convert the Cartesian equation x 2 + y 2 - 6x = 0 to a polar equation.  r² = 6cosθ r = 6sinθ r =…

A: The given Cartesian equation x 2 + y 2 - 6x = 0 ................................... (1)

Q: Find the exact area of the surface obtained by rotating the curve x = 21² +=, y = &Vr,1s153, about…

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Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

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Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

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Q: 24. The plane that contains the line x = 1 + t, y = 2 – t, z = 4 – 3t and is parallel to the plane…

A: To find out equation of plane first we change the equation of line in symmetrical form then find out…

Q: Ln (sin? (D-C)x) Using first principle find derivative of f(x) xD-C

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Q: 4. Sketch the function Ax) = 2xª – 16x², indicating any extrema, points of inflection,

A: follows the procedure given below.

Q: Use four rectangles to approximate the area of the planar region under the graph of f(x) = 0.3x –…

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Q: Find f. f"(x) = 20x + 12x² + 6, f(0) = 6, f(1) = 2 %3D f(x) =

A: Find your answer below

Q: af If f(x, y) = (18x - y)°, then is given by: 45 | 11 45 9. - 0-#(18z-유y)' 45 9. 45 O 1(18x 9. 11

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