1 sin(x) and cot(x) = is a constant number. Recall that csc(x) = 3 cot(x) The ratio dx csc² (x) (Use decimal notation.) d3 cot(x) dx csc²(x) cos(x) sin(x)

Q: Determine whether the sequence converges or diverges. If it converges, compute the limit.    an =…

A: Use ratio test

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: Differentiate: arcsin (# )+ 0 1 (E) None of these O x/y O y/x 00 + arccos (-) = 1

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Q: and the magnitude of the given vector. (-4, 4, 7)

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Q: 1 HW Score: 0%, 0 of 14 points O Points: 0 of 1 E Homework: Module 3 HW 16.4 Question 14, 16.4.33 >…

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Q: Find r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). ● r(t) = 2t²i - 2tj + = t³k (a) r'(t) (b) r"(t)…

A: Let's find.

Q: Find the integral of the following equation integrate cos(x + pi/3) dx

A: Given problem:- Find the integral of the following equation integrate cos(x + pi/3) dx

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A: We have to find the area between the loops.

Q: 43. Vertices: (0, 12), (0, −12); Asymptotes: y = ±x

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A: We have to find the value of European put option.

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [ (v - x) dx +…

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Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use ∞o…

A: The detailed solution is given below Thank you

Q: Evaluate __imit= Hint: Use a power series expansion. lim z 0 e-32³ 1+3x³ 71⁹ 9 2 o..

A: Given problem:-

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A: The given integral is x2/3 +8 limit from 1 to 2.

Q: Suppose that 3 ≤ f '(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of…

A: Given problem:- Suppose that 3 ≤ f'(x)  ≤5 for all values of x. What are the minimum and maximum…

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A: Here we have to use the concept of the trigonometric ratios

Q: (a) Estimate the area under the graph of f(x) = 2 cos(x) from x = 0 to x = x/2 using four…

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Q: Find the magnitude of the given vector. (-4, 4, 7)

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Q: Determine whether the following Consistent or not a) 5x +2y = 1 3x +2y = 1 b) X₁ + X₂-2X3 + X4 = 9…

A: Here, to check whether the given system is consistent or not.

Q: Given: xe² + In(x - y) = . Find dy/dx. Given: y = (In x), find dy/dx. Find the derivative of f(x) =…

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Q: Find the horizontal and vertical asymptotes of the curve. 6x²+x- - 9 у x² + x - 56 X = (smaller…

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Q: Solve the D.E ý - y = x لم

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Q: (D² − 4)y : 4)y = 8e²x - 12 Your answer

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: If f(3) = 11 and f '(x) ≥ 3 for 3 ≤ x ≤ 7, how small can f(7) possibly be?

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Q: nd the area between y = 8 sin x and y = = = 10 cos x over the interval

A: Topic:- application of integration

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A: In this question we have to find the value of s(t).

Q: Determine whether the sequence converges or diverges. If it converges, please compute the limit.…

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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A: Explanation of the answer is as follows

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: по + y³ =1, Dzy 2. = .:3 _ x+2y x-2y 3. : . + Злаb2, у" У X sla .

A: We can solve this as follows:

Q: Determine whether the series is convergent or divergent. If the series is convergent determine the…

A: Given problem:-

Q: Write the given (total) area as an integral. • The area above the x − axis and below y = 4 − x²

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Q: 2. Moderate Find the inverse Laplace transform of s² +8s +27 (s + 1)(s2 + 4s +13)

A: To find the inverse Laplace transform of s2+8s+27s+1s2+4s+13.

Q: c) The equation of a curve is y = √5x+4 i. Calculate the gradient of the curve at the point where x…

A: Gradient: The gradient is a synonym for "slope." The steeper the line is at the place the higher is…

Q: Applying the First Derivative Test In Exercises 29-36, (a) find the critical numbers of the function…

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Q: Find the exact length of the curve. X = v 3 y (y - 3), 16 ≤ y ≤ 25

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Q: alyze and sketch a graph of the function. Label any intercepts, relative extrema, y = x² - 8x + 37…

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Q: Check the function y=x²+1 whether have a symmetry about x or y axis

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Q: Find the arc length L of the graph of r(t). L = r(t) = 11 cos(t)i + 11 sin(t)j + tk, 0≤t≤ 2π

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Q: Determine whether the series is convergent or divergent. If the series is convergent determine the…

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Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. 3x + 4 t…

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Q: 32-37 FOURIER INTEGRALS AND TRANSFORMS Sketch the given function and represent it as indicated. If…

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Q: d² y +3-10y=3x² dx² dx

A: Given; d2ydx2+3dydx-10y=3x2 So, we can also write as; D2+3D-10y=3x2 So, the auxiliary equation is:…

Q: 2. Find the indefinite integral (Scos(4x) + √x dx

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