Calculate / cot cot³(x) csc³(x) dx. Your answer should be in terms of x.

Q: Use Green's Theorem to evaluate the following integral. So (et² + - 20y³) dx + (3y7 - 20x³) dy where…

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Q: Use a table of integrals to evaluate the following indefinite integral. The integrals may require…

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Q: B. Using the definitions of limit and/or infinite limit, show that if limn→∞ sn = ∞, then also…

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Q: Differentiate f(z) = <= COS f'(x) = Question Help: Video Submit Question (4z). Use exact values.

A: We can find the derivative using the required formula in the below steps.

Q: Suppose the function y = f(x) is defined by an equation x² + y² + sin(xy) = 9. Given that f(0) = 3.…

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Q: Find the arc length of the curve below on the given interval. y=2x³/2 on [0,9] Which of the…

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Q: Find all complementary functions of the equation y" -6y' +9y=0. a. cos3x,sin3x b. e-3x.e³x C. e-3x…

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Q: n a research experiment, a population of fruit flies is increasing in accordance with the…

A: We know that exponential  growth formula, A=Pekt Where P is initial polpulation t is time k is…

Q: Work Problems ) Let r(t) = (√√9-1, ¹5, 2t In t). (1) A) Find the domain of r(t). B) lim r(t) =? 1-2…

A: Note : As per our Guidelines , we can solve first question as your question solution not too small .…

Q: lim t→∞0 (1- 314 t t

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Q: A particular solution of 2y" + 4y' + 7y=x²

A: The given equation is; 2y''+4y'+7y=x2

Q: for each In Problems 21-30, find an explicit formula a, = sequence, determine whether the sequence…

A: The given sequence -1, 23, -35, 47, -59,..... We have to find the explicit formula for the sequence…

Q: Solve for the indicated variable. - kt X y Solve for t. 1. In In y 2. In =-kt Solve for y In 3. x =…

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Q: 1. Find the particular solution for the D.E. = 2 sec²x tanx given that dx² when x = 0, y = 0 and…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Use linear approximation to estimate 1 √117 Give your answer as a single rational number.

A: Linear approximation of a function f(x) at a point x=b is giveb by f(x)=f(a)+f'(a)(x-a)

Q: Make a sign diagram for the derivative of the function f(x) = x3 - 3x2 -24x+7 including all open…

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Q: An airplane has an air speed of 227 miles per hour and a compass heading of 140°. A steady wind of…

A: Given:  V = air plane speed vector with magnitude 227 miles per hour and  heading of 140o  . W= wind…

Q: Suppose that the cost, in dollars, for a company to produce x pairs of a new line of jeans is…

A: Given the cost functionC(x)=6500+6x+0.01x2+0.0002x3   We need to finda.Marginal cost…

Q: (fof-¹)(x) = 26² 3x 2 -44x+1 2 3(3x² + 4x +) 2 )-1 44

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Q: Prove the following integral converges to 1/2. et So dx (1 + ex)²

A: Use substitution method to solve

Q: If a stone is thrown up at 13 meters per second from a height of 190 meters above the surface of the…

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Q: (b) Use the gradient to find the directional derivative Du f(x, y) of f(x, y) = 4xy + 3y² at P = (2,…

A: Given: fx,y=4xy+3y2 We know that the gradient is just the vector of partial derivatives.

Q: Compute the line integral of the vector field F = (3zy-¹, 4x, −y) over the path c(t) = (et, et, t)…

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Q: -10 -5 lim f(x) = 811x y -5- 0 Provide your answer below: --5- 5 10 X

A: We need to find limx→-∞f(x)

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x-² In(x),…

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Q: Find the limit algebraically. lim h→0 f(-6+h)-f(-6) h where f(x) = - 8x² + 8x - 7

A: see below the answer and calculation

Q: Use the Ratio Test to determine whether the series is convergent or divergent. Identify an Since lim…

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Q: The shaded region in quadrant I is enclosed by the circle x² + y² = 4 and the lines y = V √2 and x =…

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Q: Find the equation of the tangent line on the curve x² + y² + 2y = 0 at (0, -2). A B с D x=0 y=-x…

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Q: 7. Differentiate: R(t) = tan(t) + t²tanh(t).

A: To differentiate the following function.Rt=tant+t2 tanht

Q: D Question 38 Let A = 03 O-11 O 11 O-3 [23 3 2 -17 4 13 1 Find C32.

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Q: what if it's going up by ten percent more ? not 10$

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Q: Determine where D is the region enclosed (5, 0, 0), (0,3,0), (0, 0, 3), by the tetrahedron with…

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Q: Question number 23 please

A: We have to find the local extrema.

Q: A farmer is constructing three equally-sized pens against the side of a barn for his animals, as…

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Q: For the function f(x) = -7x² + 9x + 4, find the equation of the tangent line at x = 4.

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Q: A particular solution of x²y' - x(x + 2)y' + (x + 2)y=2x³, x>0, y₁(x)=x, V₂(x)= xex

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. Identify ak Evaluate…

A: The given series is summation of 8/k!, k from 1 to infinity.

Q: 4. The table below gives the sales in millions of dollars for jogging and running shoes in the US…

A: We need to find quadratic model. As per Bartleby guidelines we can do 3 subparts. Please upload…

Q: ← - 10 -6 –4 -2 10 8 6- 4 Y 2 -2 $ + x 10 Identify the x-coordinate of the absolute minimum of f(x)…

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Q: ifferentate: f(x) = COSX 1+sin x Apply the quotient ru

A: Topic:- application of derivatives

Q: The graph of f'(x) is given below. On what interval(s) is the value of f(x) increasing? Give your…

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Q: Find the following using the table below. I 2 3 4 1 f(x) 4 2 1 3 f'(x) 4 2 1 3 g(x) 4312 g'(x) 13 24…

A: Given query is to find indicated derivative.

Q: Show that x = cos x has at least one solution in the interval [0,2].

A: Topic:- Geometry

Q: (9) f(x² - & 8x + 3)dx (h) f(ax + + b)dx ff f(²x² (i) 7x + 4e -3dx

A: Here we have to find the integration using basic properties.   Part- g Now, ∫(x2-8x+3)dx=∫x2 dx-8 ∫x…

Q: = [² If f(x) = then f(x) f'(x)= f'(-2) = -1 to dt

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Q: Write the first three terms of the sequence whose nth term is given by the formula. 1. an-n-1 1 4n…

A: To find the first term , we need to substitute n =1 in an . For second and third term substitute n=2…

Q: Consider the function Evaluate the following (a) f(5) (b) f(x) + f(5) (c) f(x-2) 3 f(x)=2x² +9x+3.

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Q: Use a trigonometric substitution to calculate a non-zero constant. X √x² + 2ax dx, where a is

A: The given integration is: ∫xx2+2axdx Use a trigonometric substitution to find the value of the given…

Q: Find the relative maxima and relative minima, if any, for the function f(x) = (x − 1)²/3 — (x +…

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