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Q: Let W be the region between the sphere of radius 5 and the cube of side 1, both centered at the…

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Q: y (5-x) 2 6) Verify Rolle's Theorem on [0,5] for the function f(x)=x√5-x and algebraically determine…

A: We have to verify the Rolle's theorem and then find values of c. According to Rolle's Theorem, if a…

Q: F(x)=√√x g(x) = 2x (f/g)(x) = domain= X

A: F(x) = (x)1/3 g(x) = 2x fund   (f/g)(x) = ?

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(x) = ["²₁ √²³ + ¹³dt…

A: given f(x)=∫-1xt3+13dt

Q: #23) y'(x) = 4 tan 2x-3 los x Saj (x) dx = S 4 tom 2x - 3 los x dx 3(x) = 4 S sin 2x dx - S3 losx.…

A: Here your answer is,-2lncos2x-3sinx+Cand the answer given in the book is,2lnsec2x-3sinx+C Here both…

Q: Solve this without using u substitution

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Q: The average value of the function f(x)=√x+2 on [2, 7] is equal to Select one: O True O False 38 15

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Q: 5x² 이 sin (8x) dx = 5 1 xcos(x) + 1 256 (8xsin(x) + cos(8x)) + C

A: We need to integrate: ∫5x2 sin8x dx We can solve this using integral by parts.

Q: Find dy dx y [A] ₁-2y 1-e²y [B] y+1 1-2e²y [C] e²y + x = y 1 1-2e²y [D] y-1 1+2y [E] 1 Ti 1-ey

A: We can use the concept of implicit differentiation Given function e2y + x = y

Q: The motion of a point on the circumference of a rolling wheel of radius 5 feet is described by the…

A: a) To find the velocity vector of the point, we take the derivative of the position vector F(t) with…

Q: Use the chain rule to find the derivative of You do not need to expand out your answer. 13 3(-5x5…

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Q: Find the equation of the tangent line to the curve y = 6 sina at the point (7,3). The equation of…

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Q: = y. Find the area of the region between the curves 4x + y² = 12 and x = Area between curves =

A: The equation of the curves are as givena) 4x+y2=12 and x=yb) y=4sinx ,y=4cosx form x=0 to x=0.4π

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

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Q: Find the distance traveled by a particle with position (x, y) as tvaries in the given time interval.…

A: For solving the given problem:

Q: The area of a circle, A=², changes as its radius changes. If the radius changes with respect to…

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Q: Determine whether the given differential equation is exact. If it is exact solve it directly. If it…

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Q: What is the area (in square units) bounded by the curve y² = x and the line x-4=0? A. 30/3 B. 31/3…

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Q: ate The following matrix shows the probability that a student will eat in the cafeteria (C) or…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Evaluate the following indefinite integral. S e13y dy 6 + e26y help (formulas)

A: The given integral is e13y/(6+e26y)

Q: Find the directional derivative of the function f(x, y) = ln(x + y³) at the point (-3, 1) in the…

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Q: Simplify and write the trigonometric expression in terms of sine and cosine: 1 tan x csc X = f(x)…

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Q: Step 7 Then when 3 units are produced and sold, the price per unit is 189 dollars, and the total…

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Q: Use the given acceleration function and initial conditions to find the velocity vector v(t), and…

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Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

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Q: The decay of a radioactive substance can be represented by more than one exponential model. explain.

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Q: Find an equation of the tangent line at each given point on the cu x = 2²2²-4₁ y = t²2 - 2t at (0,…

A: Find an equation of the tangent line at each given point on the curve.  x=t2-4 , y= t2-2t  at (0,0)…

Q: Determine the Laplace transform of the solution to Jy" - 4y + 2y = g(t) [y(0) = 8, y'(0) = 0 where…

A: The given differential equation is:y''-4y'+2y=g(t)y(0)=8,  y'(0)=0where:g(t)=0…

Q: 6x-4 if x ≤4 Suppose f(x) = -8x+b if x>4 Find the value of b so that f(x) is continuous. b

A: f(x)=6x-4x≤4-8x+bx>4

Q: Determine the composite function fog and gof. For each composite function state the domain and…

A: Here given that f(x) and g(x)  are two functions and we find composite function or f0g and g0f.

Q: 5) Graph f(x)=x²-1x-6 Clearly show all zeros, y-intercept, and end behavior

A: we have given function f(x)=x2-x-6 To Find: Zeros, Y-intercept, and end behaviour

Q: f Evaluate S Op ² 2+cos i

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Q: Let f(x) = logox and g(x)=₁*. For all x g(x).

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Q: f(x, y) = 2x² + 5y² fa(4, -3)= Calculator Check Answer

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Q: An international airline has a regulation that each passenger can carry a suitcase having the sum of…

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Q: The total surface area of the box is 5400 square centimetres, let x be the width of the box and h be…

A: The total surface area of the box is 5400 cm2

Q: (a) Find parametric equations for the line through (5, 2, 4) that is perpendicular to the plane xy +…

A: x-y+2z=1 px0,y0,z0=5,2,4 Line through Point px0,y0,z0 is perpandicular to the plane x-y+2z

Q: Farmer Jones and his wife, Dr. Jones, decide to buil a fence in their field to keep the sheep safe.…

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Q: Use the sum and difference identities to determine the exact value of the following expression. If…

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Q: The diagram shows part of the graph of y - The area of the shaded region is 6 units. Calculate, by…

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Q: Find r'(t), r"(t), r(t) r"(t), and r(t) x r"(t). r(t) = 32²1 - 4tj + 12³k (a) r(t) (b) r"(t) (c)…

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Q: f(x)=√x 9(x)=2x (ftg)(x) =

A: F(x)=x3 And   g(x)=2x

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

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Q: Let f(x, y) = -L²₁ fx(x, y) = fy(x, y) = 89 + 10 dt. Find f(x, y) and f(x, y).

A: The given integral equation is: f(x, y)=∫xy 89+t10 dt

Q: find the average Value of the function. 2 f(x) = x²-11 on [0,3]

A: We need to calculate the average value of the functionf(x)=x2-11 on [0, 3]

Q: Evaluate A. 2/3 B. 4/3 */2 12 000 C. 1/3 D. 5/3 [zdz r²dr sinu du.

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Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, -1)

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Q: ind each limit. f(x, y) = = (a) 3 (b) 1 3 x²y x + y lim Ax → 0 lim Ay → 0 f(x + Ax, y) = f(x, y) Ax…

A: We need to evaluate the limit of given f(x,y).

Q: Given the matrices A and B, compute B. A. A = 2 3 -1 5 B = 1 -3 -2 -4 Enter element in row 2, column…

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Q: 1. Evaluate each integral by first making an appropriate substitution. 1/3 (a) √ x(x² − 1)¹ dx__(b)…

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