1. Sketch the region enclosed by the given curves: y = e*, y = x² – 1, x = -1, x = 1. Find the area of the region.

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A: This is a problem of integration of the function. Please follow the procedure given below.

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A: See the answer below

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Q: For items 3 - 7, use permutation or combination in solving the problems below. Many ways C O لصنجممد…

A: Total people: 9 godmothers, 9 godfathersArrangement around a round table.  Solution:  Fix one…

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Q: 3/2 5. Find the exact area of the surface obtained by rotating the curve x =- Show All Work and Give…

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Q: state whether Converges diverges

A: To state whether the given series converges/diverges. ∑n=1+∞-1nnnsinn1n2n

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A: This is a problem of a trigonometry. Based on application of trigonometry. Please follow the below…

Q: 3 b. Compute the integral S 6x 2 dx using a limit of Riemann sums. Use right endpoints as evaluation…

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Q: Determine whether the following converges or diverges. n 2n +1 n=1

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Q: : s ech[In cosx]tanx dx Evaluate: A None - 2 tan-1(cosx) + C 2 tan -1(e cosx) + C CoSx (D - 2 tan…

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Q: Q2) Solve the D.E xdy + (2y – x* + 3x)dx = 0

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A: The given series is: ∑n=1∞4+cos2n3n-n3

Q: Graph the sinusoidal function using key points. 41) y = 1 + cos x 2- 1 -2n TC -1- -27 42) y = 4 sin…

A: Let's find.

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Q: If m < f(x) <M for a <x s b, where m is the absolute minimum andM is the absolute maximum of f on…

A: We need to find smaller and larger value.

Q: dy Find dz and simplify: y=ln[tanh(ax)] where a = constant

A: Topic = Derivative

Q: 2x3 – x² + 2x – 2 dx x²(x² – 2x + 2) - -

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Q: Determine the derivative of each function using the limit definition. 1. Y = 2 – 7x - 2 = 4 – 5x –…

A: f'(x) = limh→0 f(x+h)-f(x)h.

Q: dy Find dz and simplify: y = ln(2x + V1 + 2a²)

A: The objective of the question is evaluate the derivative of the given function.

Q: Find the derivatives using Trigonometric Functions 4 y = cos* t – sin* t \1/2 ソ= v = (2 tan² 20 –1)"

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Q: Given: (-3)"(x – 2)" Vn + 2 n=0 7 Use Alternating Series Test to show that the series converges when…

A: The given series,        ∑n=0∞(-3)nx-2nn+2

Q: 2. A rock thrown upward has a height given by s(1) = 49t-9.81 where s is in meters and / is in…

A: Use derivative to solve

Q: 3. Hallar una serie de potencias centrada en c = -3 para la función f(x) = 1 2х-5 a) Σ (3x)* 2-1…

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Q: An irrigation sprinkler in a field of lettuce sprays water over a distance of 25 feet as it rotates…

A: We are going to slove above question and find the area of field

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Q: -1 4 1). -dx = -3

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Q: CoS“ n In n а. n2 n³ n=1

A: Solution: a) ∑n=1∞cos2(n)n2+ln (n)n3

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A: We have to find the value of the given integral.

Q: 3" e" – 2" n=1

A: The given series,        ∑n=1∞3nen-2n

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Q: Express the integrand as a rational function and then evaluate the integral. x - 4 dx Jo x² – 5x + 6

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Q: An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) = 65e-0.02t…

A: Given: r(t)=65e-0.02t Now, 1 hour=60 minute The amount of oil leaked in first t minutes is ∫0tr(t)…

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A: we know that sin θ   is negative in 3rd  and   4th  quadrant quadrants. tan θ   is negative in 2nd…

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A: Solved below

Q: Solve the equation 4cos2B – 4cos B = 3 given that 0 < B < 2r. Provide your answer below:

A: We have to solve the quadratic equation, it's roots will give value of the solution

Q: 2. Find the area of the region bounded by y = e*, x = 0, x = 2, y = 0 using definite integral %3D…

A: This is a problem related to integration application. Based on general formula we will solve the…