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Q: π 7. fz sin¹x cos¹ x dx

A: To evaluate the following integral by using Walli's formula.∫0π2 sin4 x cos4 x dx

Q: Let a = . Find al. Check Answer

A: Given a→=<5,-1,-4>To find: a→

Q: Let à = (-2, 2, 3) and 6 = (4, - 1,5). Find the projection of b onto a. proj, b =< Check Answer

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Q: Let w(x, y, z) = x² + y² + z² where x = sin(7t), y = cos(-3t), z = e-4t. dx dy dz dw dt dt' dt dt…

A: Given problem:- wx,y,z=x2+y2+z2,x=sin7t,y=cos-3t,z=e-4t Find dwdt

Q: 7. Find: y = In dx √6x-5 [ Lex (x+1)³.

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Q: Exercises: Use the theorems on limits to evaluate each of the following, if it exists. 1. lim (2x³…

A: See this solution in below.

Q: 2. The piecewise function g(x) is defined as follows (x+2)³ g(x) = cos(x) (x-1)²/2 if x 1. (a)…

A: Please see the below picture for detailed solution.

Q: Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started…

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Q: 1. Simplify the following: a) b) 8 45x X 3 15y 20y 18x 2 (x² − 9) 5 2 x+5x +6

A: Recall: a2-b2=(a+b)(a-b)

Q: 4. If ricost cosh t+j sint sinh t, where i and j are constant orthogonal vectors prove that (a)…

A: Given r = i cost cosht + j sint sinht

Q: Use spherical coordinates to evaluate the triple integral D Answer= pi(0.2147)(2) E -(x²+y²+z²) /x²…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 17 -…

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Q: Find the area under the curve y 9 x over the interval [1, 5]

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Q: Evaluate the definite integral. 1³ sin (4t)dt

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Q: 7. lim x-1x³ 2x²-x-3 + 2x² + 6x +5

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Q: 2. Compare the rates of growth of f(x) = x + sinx and g(x) = x as x approaches infinity. f(x) grows…

A: The given functions are fx=x+sinx and gx=x we have to compare the rate of growth as x approaches to…

Q: 6. a) State why the limit of f(x) = √5x - 1 does not exist for x

A: Please refer to the image below

Q: 1. Find the area under one arch of the curve y = cos- :cosex.

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Q: The surfaces p= 3 and 5, p = 100° and 130°, and z = 3 and 4.5 identify a closed surface. (a) Find…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3. Evaluate f(x) = 15 – ½ (x) for f (4). a) 16 b) 14 c) 13 d) none of the above

A: 3.  This is a problem of polynomial.  Here given a polynomial f(x) and find f(4).

Q: 1/5 a) S J1/10 10 Arc sin(5x) dx

A: Please see the below picture for detailed solution.

Q: 9. Find the area bounded by a parabola and any right chord. (Use the parabola y² ax, chord x = x1.)

A: solution is given below..

Q: For the function f(x)= −2sin(x−3π/2), determine its amplitude and period, and then graph it for two…

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Q: A colony of bees lives in an ever-growing beehive that is in the shape of a sphere. Use The volume…

A: 20 new bees are added to the hive each week. Each bee in the colony needs 5 cm3 of space. (space…

Q: What is the radius of convergence of the series R=2 b. R=1 R = ∞ d. R=0 a. C. +∞ xn n+1 -?

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Q: Part 1 A rectangular tank with a square bottom has base side lengths of 3 feet and a height of 10…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Evaluate the triple integral W z dV where E is the solid bounded by the cylinder y² + z² = 100 and…

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Q: 7. Evaluate f(x) = 9 - 8x for f(-3). a) -15 b) 33 c) 20 d) none of the above

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Q: In a cafe, only coffee and tea are offered. The probability of a customer buys a cup of coffee is…

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Q: A tank half-filled with water is in the form of a rectangular parallelepiped 5 ft deep, 15 ft wide,…

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Q: Answer: Use a triple integral to find the volume of the solid enclosed by the paraboloids y = x² +…

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Q: Find the point at which the line y(t) z(t) = 2 + 4t -6-8t intersects the yz plane. 6-7t

A: The line x(t)=2+4t, y(t)=-6-8t, z(t)=6-7t intersect yz plane Note:    Multiple questions are given,…

Q: You will construct a fenced in area along the side of a building. The pen will be in the shape of a…

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Q: 4. Which of the following is f(x) = x² the parent function for? a) f(x) = x³ + 2x²-x+ 13. b)…

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Q: Suppose R is the solid bounded by the plane z = 5x, the surface z = x², and the planes y = 0 and y =…

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Q: Determine it each of the following is absolutely convergent, Conditionally convergent, for…

A: We have to test whether the series is absolutely convergent conditionally convergent or Divergent.

Q: 5. 6. 7. 8. √√x-1 lim- x-1 x-1 x³-x²-x+10 lim X4-2 x²+3x+2 2x²-x-3 lim x-1x³ + 2x² + 6x +5 lim…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Let à = (1, -2, 0) and 6 = (1, 3,2). b Find the angle between the vector (in radians) Check Answer

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Q: Basic Level 1. The graph shows the total cost of making compact discs. 250 Namibian Dollars…

A: According to the graph :-cost of 0 compact disc=N$50 thousandscost of 5 thousands compact disc=N$80…

Q: . Given TR = 45Q -0.5 Q², TC = Q³-8Q² + 57Q + 2, find out the level of : output at which firm…

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Q: Given f''(x) = 5x - 2 and f'(-2) = Find f'(x) = and find f(1) - 4 and f(− 2) = 4.

A: Topic = Integration

Q: 2. d. lim f(x) = e. x-0+ f lim_f(x) = lim f(x) =

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Q: Find the arc length of the curve on the interval. r(t) = (3 sin(t), 7t, 3 cos(t)), 0 ≤ t ≤ The…

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(x + 5y + 6z). F(x, y, z) = =

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Q: (b) If f(x)= |x-1| is now restricted to the domain x ≥1, find f¹(x) and state its domain and range.

A: Given problem:- If fx=x-1 is now restricted to domain x≥1, find f-1x and state its domain and range

Q: Find SS₁² 6x d.A over the region R = {(x, y) | 0≤x≤ 2,0 ≤ y ≤ 5} by identifying it as the volume of…

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Q: Find Ž k=0 the convergence Set for each

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Q: Suppose that f(x, y) = 5, and D = {(x, y) | x² + y² ≤ 1}. Then the double integral of f(x, y) over D…

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Q: 4. Find the area bounded by the curve a²y = x³, the x - axis, and the line x = 2a. Solve in two…

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Q: Find the curvature of the curve r(t) = (5 + 4t, 4 - 4t, 1 - 3t) at the point t = -6. Check Answer

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