Find the arc length of the curve below on the given interval. 3 5+² 4x y = 3 on [1,4]

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

A: We have to find the distance travelled and length of curve. First let us find the derivatives of x…

Q: Evaluate the definite integral. S 6xdx

A: let  B=∫026xdx

Q: ng circle. Then, write the equation of the circle in both Standard -8 -6 y 6 + 4 24 -4-20 -6+ -8+ N…

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Q: A particle moves with a velocity of v(t) ft/s along an s-axis. Find the displacement and the…

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Q: Prove that if (c, f(c)) is a point of inflection of the graph of f and f''bexists in an open…

A: To prove that if c, fc is a point of inflection of the graph of f and f'' exists in an open interval…

Q: Find the derivate of the function: (using the Power hule of functions on a and b) a) F(x) = (x² - 6…

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Q: X = x = 83 logg 4-logg 9 Note: Your answer must be exact and in simplest form.

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Q: Find the tangent plane to the equation Z= 5y cos(4x - 6y) at the point (6,4,20)

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Q: O (√x-x² + 2)dx 2

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Q: Find a potential function f for the field F = 5y + 32 (2 1 + 10x j+ 6x k). A general expression for…

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Q: Evaluate the following definite integral. Express your answer in terms of logarithms. dx 2 1…

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Q: 6. A farmer would like to create a rectangular pen to raise rabbits. The fencing for the north and…

A: To find out the dimensions that would maximize the area of the pen.

Q: A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a…

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Q: b) Y = -10x³ + 3x² + 4x +3

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Q: A particle moves in the coordinate plane with position vector (x(t), y(t)) such that x(t) = t² - (t)…

A: Note : Since you have posted a question with multiple subparts, we will provide the solution only to…

Q: Question 8 Let h be differentiable at 4 with h(4) = −1, h'(4) = 1. Let f(x) = x³h(x²) for all x.…

A: Given that h is differentiable at 4 with h(4)=-1, h'(4)=1.Letf(x)=x3h(x2)We need to calculate f'(2)

Q: y = f(x) = = x = g(y) = 4 – 7x 9 - 9x h

A: step 1: Write f(x) as y . step 2: swap 'x' and 'y' . step 3: solve for 'y' .

Q: f(x) = √√/23 — x. Express with interval notation, using U for the union of sets and inf for ∞.…

A: f(x) is given, we have to find Domain and range of this function.

Q: Differential equations. answer. Please show your work S Second picture is the 8. Solve y''+4 y'+5…

A: y''+4y'+5y=16cos(2t)+2sin(2t) The general solution can be written as: y=yh+yp

Q: Suppose that in the interval 13 ≤ ≤ 18 you know that f'(x) is positive and f(x) is negative. Select…

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

Q: Prove: Proof: lim x 0 (x² cos (²7)) = 0. COS

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Q: Charles 'n Marge sell custom-build cabinet units for motor homes. The function P(x) = -1x² +800x -…

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Find the final amount in the following retirement account, in which the rate of return on the…

A: For the First four years The amount is $408 per month at r=6% For the Second 4 years The amount is…

Q: Find the derivative of the function. h(x) = x² arctan(9x)

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Q: 1² 2t 1+1² 1+1² A submarine is traveling such that its position vector s(t)=, where s is in miles…

A: A submarine is traveling such that its position vector st=t21+t2, 2t1+t2, where  s is in miles and t…

Q: Question 10 a) In the expansion of (2+2cx)6, the coefficient of the x³ term is the same as the…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Directly compute the line integral xds over the helical curve C: r(t) = (t, 2 cost, 2 sint) as 0≤t≤.

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Q: Find y @) y ² y's SX-2 Sin (x) b) 2 Y = 2 cos (x)-x

A: To find the derivative each of the following functions. (a) y=5x-2 sinx (b) y=2 cosx-x2

Q: ← dy Find for the following function. dx dy dx 5 cos x y=8-9 cos x 11 40 sin(x) (8-9 cos(x))²

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Q: Find a potential function f for the field F. F= (Inx+ sec 2 (2x+2y))+ sec 2 (2x+2y) ++ 3y 3z 2x2) 1*…

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Q: sin COS tan 19 19п 19п 4 = = = 18. Пур

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Q: Find the slope of the tangent to the graph of x² 4 f(x) = at the point (-2,0). Write x² + x + 1 your…

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Q: form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros:…

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Q: Use the remainder theorem to find the remainder when f(x) is divided by x+3. Then use the factor…

A: Given f(x)=3x6-27x4+x2-8 to be divided by x+3. To find the remainder using the remainder theorem.…

Q: Find the derivative of the following function. 5. f(x) = - cosh *3x

A: The given function is ƒ(x) = - cosh5(3x)

Q: K The length of a stalactite (in mm) has been measured at the beginning of every fourth year since…

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Q: Rewrite sin55° in terms of the appropriate cofunction.

A: Consider  sin(55°)

Q: For a small farm, the cost in dollars to produce a containers of ice cream is C(x) = 0.7x + 40. The…

A: Given the question :-C(x)=0.7x+40, Demand function ,in dollars p(x)=19.564-0.006x

Q: •S xy dx + (x + y)dy along the curve y=x² from (1.1) to (2,4). Evaluate √xy dx + (x+y)dy = с (Type…

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Q: Which of the following represents the area interior to both r = 5-5 sin(0) and r = 5 sin a) 102 (…

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Q: Find f. f(x) = f'(x) = 24x² + 2x +4, f(1) =1, f(1) = −4

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Q: 15. on the interval (012), the function y = x³ + 3x2 - 4x +27 has an absolute max when X= A. 2 В. О…

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Q: Find the directional derivative of the function at the point P(2,1) in the following direction:…

A: The given function is:f(x,y)=3x2y-2xy2+y3-9P=(2, 1)Direction vector:  v=3i-5j

Q: Question 10 lim (1 + 5x) ¹2 x →0 =

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Q: The upper half of the ellipse centered at the origin with axes of length 2a and 2b is b2 described…

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Q: Give the exact values of each of the following: tan (30°) = tan(45°) = N tan(60°) =

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Q: Evaluate the following definite integral. Express your answer in terms of logarithms. €² dx 2 1…

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Q: Determine for the following equations. Simplify your answers. dx a) x² + y² = 36

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Q: Suppose that f(x, y) = x² - xy + y² - 4x + 4y with D = {(x, y) | 0 ≤ y ≤ x ≤ 4}. 1. The critical…

A: Suppose that f(x, y) = x ^ 2 - xy + y ^ 2 - 4x + 4y with D=\ (x,y)| 0 <= y <= x <= 4 .

Q: Find the circulation and the flux of the field F=-yi+xj around and across the following curves. a.…

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