Given r = 1 - 3 cos 0 find the following. Find the area of the inner loop of the given polar curve rounded to 2 decimal places.

Q: e) Evaluate the following limit at infinity and show your work. 3x3-4x a) lim x→∞ x²-2x³

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Q: Evaluate the definite integral. 8 (2n-²-n-³) dn 8 (2n-²-n-³) dn=[ 4 (Type an integer or a simplified…

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Q: Find a formula bn for the n-th term of the following sequence. Assume the series begins at n = 1.…

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Q: Find a formula a, for the n-th term of the following sequence. Assume the series begins at n = 1. 1…

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

Q: air resistance can be ignored, how high does it go?

A: Given query is to find the height of the ball.

Q: There are five men and three women in a room. How many committees of 4 people can be chosen from the…

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Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² +1 a. (3,4) b. (0,3)

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Q: 9) Find the equation of the tangent to the curve y = 1+ Int and x=t+Int when t = 2.

A: Given problem:- Find the equation of the tangent to the curve y = 1 + lnt and x=t+Int when t = 2 .

Q: Find the derivative of the function using implicit differentiation.  1.) x³-3x²y+2xy²=12 2.) x²-y²…

A: This question is related to implicit differentiation, We will solve it using given information.

Q: For each given functions, find the slope of the tangent at a given point using first principle…

A: We have to find the equation of tangent.

Q: d e) (In|sin x)) dx

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Q: Find the binommal coefficient (4)

A: Topic = Algebra

Q: 2 2 dx 2x (V2x + 9)

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Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vf|(−2,2,− 1) = ₁ + Oj + k (Type integers or…

A: We want to find the gradient of the given function at point (-2,2,-1).

Q: √² (5x²-3x+18) dx 9x - x³

A: Integration is done by dividing polynomial.

Q: 1. Evaluate the given integral Q. = [] [²³² Q L L (x - y) dx dy

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Q: Find the derivative of a composite function using the Chain Rule or General Power Rule.  1.)…

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

Q: 2. Using Linear Approximation, evaluate √81.4305 using the given function and initial valu below.…

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Q: Topic: Arc Length Find the length of the arc of the function x^2 = 4y from x = -3 to x = 3. a) Graph…

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Q: 4. A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate…

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Q: 1. Evaluate the given integral Q. √x²+1 (x - y² + 1) dy dx

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Q: 3√3 dx √3 x² √√x²+9

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Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Let the length of a diagonal is = d1=x m So the length of the other diagonal = d2=(x+2) m. Given…

Q: 4. Determine whether the following statements are True or False? y = f(x)

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Q: 3. Suppose a function H(t) is given and that this function describes the height H of a projectile t…

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Q: Find the length of the are of the function x² = 4y from x = -3 to x = 3.

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Q: 3 fin [ ха Txx² 2 - 1/2 to

A: To evaluate: ∫13lnx21+x212dx=∫1312lnx21+x2dx=12∫13ln x2-ln (1+x2)dx=12∫13(2ln x) dx-12∫13ln(1+x2)…

Q: b) f(x) = хе-пх

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Q: dw For the functions w= -5x² + y², x = cost, and y = sint, express as a function of t, both by using…

A: Given query is to find the Indicated derivative.

Q: 6 cos3x cos4x dx

A: To evaluate: ∫π6π2 cos⁡3xcos⁡4xdx Let I = ∫π6π2 cos⁡3xcos⁡4xdx We know that 2cosAcosB =…

Q: If the population of a city is 155,000. If the population declines continuously by 5% per year, what…

A: Question-   If the population of a city is 155,000. If the population declines continuously by 5%…

Q: Find the slope and the rate of change of the slope with respect to x when t = 90°. x = 2 cos (3t)-3…

A: This question can be solved using the concept of first and second order derivatives at t=90°

Q: Find the extrema of each given function on a specified closed interval. 1.) g (x)= x³ - (3/2)x²,…

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Q: Find the largest triangle that can be inscribed in the ellipse (x2/a2)+(y2/b2)=1 using Lagrange…

A: answer is in next step

Q: dw ow For the functions w = xy + yz + xz, x= u + 3v, y = u- 3v, and z = uv, express and using the…

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Q: A rectangular swimming pool is 42 ft wide by 75 ft long. The table gives depths (d) from x = 0 at…

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Q: 4) Given the points A(1, 2, 3), B(5, 4, 3), and C(2, 1, 2), find angle C

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Q: 2. y = 1 (tanh~' 2x)3

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Q: 3. Find the member of the curve whose slope at any point is and passes through the point (1, 1)

A: The given problem is solved below in detail.

Q: d. lim+ In 1000 X X5

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Q: Consider the functions z= - ex In y, x= In (u cos v), and y = u sin v. dz dz (a) Express and as…

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Q: Topic: Area of Surface of Revolution The arc of the parabola y=x^2 from (1,1) to (2,4) is rotated…

A: We have to find the surface area.

Q: 7 =-=—=x² Find the center of mass of a thin plate of constant density & covering the region bounded…

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Q: If the population of a city is 155,000. If the population declines continuously by 5% per year, what…

A: Given query is to find the attached population after 15 years.

Q: Find the length of the curve for 12x = 4y³ + 3y-¹ where 1 ≤ y ≤ 3 Enter your answer in exact form.…

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Q: Which of the following statements about the graph of f(x) = (2.25) shown above are true? Select all…

A: Given graph of f(x)=(2.25)x

Q: 11. Find the limit using algebraic techniques. The limit of f(x) = -4 O- 0 O=¹ x+4 2x²+5x-12 as x…

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Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

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Q: S 10dz 4z3-4z²+5z

A: To evaluate the given integral: