Using an appropriate substitution, the integral [x² x² csc²(x³) cot(x³) is equal to - dx - In ³√√|cot(x³)| + C the above - Incot(x4)| + C

Q: If the angle of the moon is decreasing at 0.25 radian per hour, how fast is the shadow of a 150 ft…

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Q: Find the solution of the given initial value problem:

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Q: Find the radius of convergence, R, of the series. x4n n (In(n))² R = 00 Σ n = 2 Find the interval,…

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Q: -if f₁ (t) properties of Fourier transfor eat alt) JF.T = $ fit) ējut dt = - feat. ejust dt е ماز-…

A: Topic:- calculus

Q: Verify the identity algebraically. Use a graphing utility to check your result graphically.…

A: Here, to simplify the expression: 7cos3(t)csc(t)

Q: A linear function is given. g(x) = −6x + 2 (a) Find the average rate of change of the function…

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Q: Je ež cos (2t)dt

A: Please see the below picture for detailed solution.

Q: 4. Use absolute value notation to describe The distance between x and -10 is at least 6.

A: In this question we have to find the solution of the given statement.

Q: Find the solution of the given initial value problem. 3y"" +27y810y = 0; y(0) = 11, y'(0) = 57,…

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Q: cosh(In2)= A B C D 5 4 0 Alw Some other answer

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Q: Find the general solution of the differential equation. y"" - 5y" - 25y + 125y = 0. NOTE: Use c₁1,…

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Q: Find the area of the region common to the interiors of the cardioids r= 1 - sin 0 and r= 1 + cos 0.…

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Q: Compute the gradient of the following function and evaluate it at the given point P.…

A: Given the function  g(x,y)=x2-4x2y-5xy2 ; P-2,1

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium 100 has been reduced…

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Q: Use the chain rule to find the indicated partial derivatives. z = x² + x²y₁ x = s + 2t - u, y = stu²…

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Q: use the if f₁ (t) properties of Fourier transform ē at ult) = JF.T =jº f(t) = ³wt dt 88 Seat, ejut…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y₁…

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Q: Verify the identity. (Simplify at each step.) 8 sec x(sec x tan x) - 8 sec4 x(sec x tan x) = 8 sec5…

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Q: Given: ZBCE ZDAF, 4BCE = ADAF Prove: BCDA is not a parallelogram. Use paragraph proof. Copy the…

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Q: 1)² +5jw+6 =(jw)² + 3jw+2jw + =jw(jw + 3) + 2(jw+ (jw+3)(jw+2) How did he get the

A: Topic:- simplification

Q: Find the radius of convergence, R, of the series. x4n n=2n(ln(n))² R = 8 Find the interval, I, of…

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Q: You are planning to make an open rectangular box from a 38-in-by-75-in. piece of cardboard by…

A: This question is based on application of derivative.

Q: Use a graphing utility to approximate (to three decimal places) the solutions of the equation in the…

A: The value of the x for which the graph crosses the x-axis will be the solution of the equation.

Q: Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that…

A: The given data is: Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min To find: How…

Q: m 10. PREVIEW ONLY -- Find an equation of the tangent line to the curve y = 9° at the point (1,9).…

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Q: 3 Detennine it the following series is on divergent Convergent a 745-6 นะ ET 3n³+2n Determine if the…

A: Series Divergent Test : Consider the series ∑n=1∞ an . If limn→∞ an does not exists or non zero .…

Q: 1. f(x)=x²+2x+1 & f(x) = 2x+5

A: To find the area between the curve.

Q: The particular solution of y(x+y) dx + (x + 2y − 1) dy=0; y(0) = 2 by NEDE is A B C D x(x+y=1)=4e-x…

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Q: For the equation given below, evaluate y at the point y - 6x² + 24 = 0.

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Q: Apply L'Hôpital's Rule to evaluate the following limit. It may be necessary to apply it more than…

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Q: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time…

A: Topic- quadratic equations and application of derivatives

Q: What is the radius of convergence of a power series? How do you find it?

A: Here we have to define the what is radius of convergence and interval of convergence and how to find…

Q: Consider the vector field F and the curve C below. F(x, y) = x4y5i + x5y4j, C: r(t) = (t²- 2t, t² +…

A: Consider the vector field F→ and the curve C F→(x,y)=x4y5i+x5y4jC:r→(t)=t2-2t,t2+2t , 0≤t≤1

Q: Find the lengths of the sides of the triangle with the indicated vertices, and determine whether the…

A: A detailed solution is given below.

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 4 − x2,…

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Q: The indicated function y₁(x) is a solution of the given differential equation. xy" + y' = 0; Y₁ =…

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Q: Find the derivative, f'(x), for f(x) = S dr 3 sinr+2 (₁²³+√7) X A f(x) = B f(x)= −sinx − 2 x²³+√√x X…

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Q: If k> 0 such that O St the above 4* dx = 3 then k = 2ln 2

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Q: Consider the parallelepiped with adjacent edges Find the volume. V = i u = Si + 5j + k v = i + j +…

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Q: f(x) lim sin(5x) X I 0 -0.25 3 2 Estimate the limit numerically or state that the limit does not…

A: We have to find out limit

Q: 2. Find the Laplace Transform of each of the following. ( 2-t b. f(t) = t - 1 1 t 5

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Q: 2a It costs c dollars each to manufacture and distribute backpacks. If the backpacks sell at x…

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector.…

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Q: Suppose that f(x) = 6x + 3x². Evaluate each of the following: ƒ'(2)= f'(-1)=

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Q: 2x-√5+4x lim x→6 x-3

A: The given limit is limx→62x-5+4xx-3

Q: The equation (4x-2y+5)dx +(2y²-2x)dy =0 is a lan A Bernoulli's DE B Exact DE C) LDE of order 1 D)…

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Q: Let 8 f(x) = ΣX2 n = 1 Find the intervals of convergence for f. (Enter your answers using interval…

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Q: Test the series for convergence or divergence. (-1)^+1 n+8 n=0

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Q: dx 2+2 sin x + cos x

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Q: 1 x-1 x-1 ln x 3) lim

A: Explanation of the answer is as follows