Evaluate the following integrals: 0 (Cartesian to Polar) Given the cartesian coordinate, find FOUR Sets of polar coordinates for the point for -21 ≤0 ≤ 211 a.) (3,3) b) (3,-2) c.) (-3,√3) d.) (-3√2, -3√2) )

Q: 7π| A d) S_T/A (sin x + cos x) dx

A: We will evaluate the given integral in the following step.

Q: 2. Find the general solution o- = y(1+e³) 1 له 342433434 11 11 1 "싫

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Q: A company manufactures two products. The price function for product A is p = 20-x (for 0 ≤ x ≤ 40),…

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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: The half life of a decaying substance is the amount of time it takes for the substance to reduced to…

A: Let us assume it takes n half-lifes to reach 10mg

Q: • Evaluate the following integrals: Convert this Cartesian equation (x² + y²)²_9(x² - y²) = 0 to…

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Q: Evaluate the limit sin 2x lim 20 7x

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Q: Choose one(1) from the following question to be answer. The graph of each rule must reflect on your…

A: The Trapezoidal Rule: The Trapezoidal Rule divides the whole area into smaller trapezoids rather…

Q: b) f(x) = хе-пх

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Q: Question B2 Consider the vectors, 3 p= and q= 2 (i) Compute 3p - 5q. (ii) Find the length of p, that…

A: A detailed solution is given below

Q: 4. Find f'(x) if f(x)= In (2x) + cos (6x)

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Q: T Find the linearization L(x,y) of the function f(x,y) = ex cos (5y) at the points (0,0) and 0, The…

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Q: 2 (0) IF F(x)= x 'e', Find f'(x) and F (1)

A: Finding the derivative of the function.

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: center of the mass of a thin density covering the Constant density 8. by the x-axis and EA Y = 3/2/…

A: We have been given that curve  y =32cosx with -π3 ≤x≤π3                  and   density…

Q: Evaluate each limit if exist lim x -> 0 (\sqrt(x+7)- \sqrt(7-x))/(2x) lim x ->3…

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Q: 2. Evaluate the integrals. (a) S (b) [9rc (c) J (d) O 1+ e²r 9x cot(x²)dx -do -dx cos sin² 0 +1 -dx…

A: As per the guidelines we can solve 3 parts only

Q: 3. Find the equation of the tangent to y = 1-x² 3x+7 at the point where x = 1.

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Q: (e) [ - V TVT - 1 dr

A: to evaluate the integral.

Q: 9. f(x) = xe−2*, a = 0

A: According to bartleby guidelines I can only answer the first question of the two given.

Q: (CLO-1) Determine the horizontal asymptote(s) of the given graph. 12 10 Ox=4 and x = -4 Dy=2 Ox=2 Oy…

A: The given problem is solved below.

Q: Differentiate the following using Chain Rule. 1. f(x) = (2x - 1)4

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Find the exact values of inverse trigonometric expressions for Parts a to c in radians. Sketch the…

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Q: - 1/2 Find the gradient of f(x,y,z) = (x² + y² + z²) 23 23 26 Vf|(- i+ - (-2,2,-1) 54 |j+ 54 27…

A: The function is f(x, y, z)=(x2+y2+z2-1/2+ln(xyz)  The point is (-2, 2, -1)

Q: F- 2x-7 h(a) √√x +3 the function Find the Domain (11) Range of (11) Show wheather the function is…

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Q: This question is designed to be answered without a calculator. Let f be a function such that lim…

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Q: Siven a = (1, 2, 1) and b - (k. 1, 2) and a × b = √35. X Determine the value(s) of k.

A: Follow the procedure given below.

Q: 5. Find the limit using algebraic techniques. The limit of f(x) = 14 1/13 14 7 x²-49 as x approaches…

A: We have to find out limit

Q: RIN Find the linearization L(x,y) of the function f(x,y)=e4x cos (3y) at the points (0,0) and 0₁-…

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Q: M8 1 Σ n=1 h n’ + 8 +8 3

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Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

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Q: A cylindrical can is to be designed with a capacity of 1000 mL. Find the dimensions of the can,…

A: Given problem:- A cylindrical can is to be designed with a capacity of 1000 mL. Find the dimensions…

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 center of mass of a thin plate of constant density & covering the given region. The region…

A: Let's find center of mass.

Q: Find the center of the mass of a thin plate of constant density & covering the region bounded by the…

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Q: Practice Problem Instruction: Find the coordinates of the midpoint of a segment with the given…

A: This is a problem related to midpoint of the line segment. based on the general formula and concept…

Q: 12. What is the amplitude of the graph below? y 4 0 8+ 7+ 6+ 5+ 4+ 3++ -1- -3+ -4+ -5- -6+ -7+ -8+…

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Q: 5. y" + 8y + 16y = 0

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Q: These are separate quesitons

A: a) At x = 2, f(2) lies in the fourth quadrant where y is negative. So f(2) is negativeb) From the…

Q: We Th Fr Sa Su Evaluate the Integral 4x dx e4x +1

A: Solution of given question is written in below steps.

Q: dy 5. Use Implicit Differentiation to find dx a) 4xy + x² = 4 - Iny³

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Q: 4- у ду dx 2 ху +x = 0

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Q: This question is designed to be answered without a calculator. If g(x) = si sint dt, then g'(x) = 0…

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Q: Let R be the region inside the polar graph labeled "Inside" and outside the polar graph labeled…

A: We will find the region R covered from inside by r=8 and outside with curve r=-8+8sinθ.

Q: 3 (b) / 2³ x³ cos(x¹ + 2) dx

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Q: 1) Determine the projection of a= [5, -4, 8] onto b = [3, 7, 6].

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Q: 10.) Solve. Write the exact solution in terms of logarithms. el-3x = 4

A: This question can be solved using the concept of natural logarithm.

Q: 1- Use the shell method to find the volume of the solids generated by revolving the shaded region…

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Q: Find the gradient of f(x,y,z) = (x² + y² + z²) 23 26 Vf|(-2,2,-1) = i+ 23 54 |j+ 54 27 (Type…

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Q: Compute the center of mass/ centroid of the region R = {(x, y): 1≤x≤3, 0≤ y ≤ x²

A: Here we have to find the centre of mass of a region.