Evaluate the integral. "π/2 cos(t) √ 1 + sin²(t) dt

Q: 5 2 3. f(x) = 3x3 - 15x3 Find the intervals of increasing, decreasing 4. If xy+cos y, Find

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A: To solve this problem, we need to compute the total mass  m  of the hemisphere and the  z…

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A: Step 1:   Step 2: Step 3: Step 4:

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A: 1.To find dxdy​ for the curve given by the equation:5x2+29xy+15y2=24We can use implicit…

Q: 3. (i) Using the definition of the line integral of a vector field, calculate the line integral L³…

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A: 1.(a)We are givenx=∣t∣andy=∣3−∣t∣∣We substitute for ∣t∣ in second equationy=∣3−x∣,x≥0(b)We observe…

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A: The problem is illustrated as:It is also given that the distance x is changing at a rate of 7…

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A: Step 1:    Step 2: Step 3: Step 4:

Q: Solve the given differential equations by using the principle of superposition (D2 − 1)y = sinh x

A: Step 1:Step 2:Step 3: Step 4:

Q: 5. Carrie says: "The derivative of a cubic polynomial function is a quadratic function." Is this…

A: 1.Understanding a Cubic Polynomial: A cubic polynomial function is a polynomial of degree 3, which…

Q: Find the Laplace transform L-1 { 1 / (s2 + 1) (s2 + 16) }

A: Step 1:    Step 2: Step 3: Step 4:

Q: Describe the regions whose equations in cylindrical or spherical coordinates are given below—either…

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Q: only part e needs an answer.

A: To find where the function f(x)=x4−9x3 is decreasing, we need to determine where its derivative,…

Q: The graph of f is shown for the interval [-2, 6]. 45 40 35 30 25 20 15 10 5 0 54 y x' -3 -2 -1 0 1 2…

A: Step 1: Understanding f′<0 and f′′>0f′<0: This means the function is decreasing over that…

Q: Question 3 1 pts By changing to spherical coordinates, calculate A = SSS, e(x²+y²+z²)³/2/2 dV, = 2x…

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Q: 2. Which of the following differential equations has the direction field shown? Explain your answer…

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Q: Free Response Question-1 Calculator NOT Allowed 2 D 2 E F 4 Graph off G t -S g(x) <-4 -2 2 G 1 4 8 2…

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Q: Please help me answer questions 1-18. I've been searching the internet and I know this is really…

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Q: Please help on all asked questions. Please show all work and steps. Please circle the final answer.

A: Approach to solving the question: A vector quantity has both magnitude and direction.A scalar…

Q: 5. Submit answer Practice similar X Compute T2(x) at x = 0.6 for y = e and use a calculator to…

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Q: 2sec^2x-2sec^2x•sin^2x-sin^2x-cos^2x=1

A: Step 1:It is needed to prove the following identity:2sec2x−2sec2x.sin2x−sin2x−cos2x=1 Now, the…

Q: 1.4 points Evaluate the definite integral shown. You must show enough work to convince me that you…

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Q: ASAP 1

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A: a. As x approaches 2 from the right, f(x) approaches -1.b. As x approaches 2 from the left, f(x)…

Q: b) Ving after July). (2) c) what kind of time will: lation (5) 5) A bank advertises that it…

A: Because the bank employs continuous compounding, your money will increase steadily over time. We…

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Q: Test the series for convergence or divergence.

A: Step 1:The provided series is:∑n=1∞​n!3nn2​It is needed to test the series for convergence or…

Q: (b) For each of the following sets, 6 is an element of that set. (i) {x ER|x is an integer greater…

A: Let R denotes the set of all real numbers and Z denote set of all integers.If an element a is a…

Q: I'm doing a partial derivative series of the area (A) of a triangle. We have two sides (a and b) and…

A: When you do derivatives, there is no way you can get the same answer. It is important to know that…

Q: Find parameterizations for the following paths from the point (1, 0, 0) to the point (−1, 0, 0).(a)…

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Q: A particle starts at the origin with initial velocity v (0) = (1, −1, 3). Its acceleration is a (t)…

A: Step 1: Given-The initial position of the particle is r(0)=(0,0,0) (Particle starts from rest.)The…

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A: The function given is f(x)=3x-10 and the interval is from x=2 to x=8.

Q: Use integration by parts to determine which of the reduction formulas is correct. O 6 sec (x) dx = 6…

A: To verify which reduction formula is correct using **integration by parts**, let's proceed step by…

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Q: 3. Consider the following system of equations, x(t) = (x, y), - x' = (3-1)x 5y y' = 2x+(3+ 1)y (a)…

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Q: Evaluate (2x+3y+z)dV, where E is the solid in the first octant under the paraboloid z = 9-x²-12. E…

A: Step 1:Step 2:Step 3: Step 4:

Q: find the Laplace transform. Then express the given function f in terms of unit step functions

A: GIVEN : ​​ STEP : 1 ​​ STEP : 2 ​​ STEP : 3 ​​ STEP : 4 ​​ STEP : 5 ​​ STEP : 6 ​​   Let's express…

Q: 3. Submit answer Practice similar Calculate the integral approximation Se for So dz. L-de 4 1.…

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Q: Consider the second order linear differential equation ty" -2y' + t² y = 0 Let y1(t) and y2(t) be…

A: Step 1:Step 2:

Q: Calculate the arc length of y = 5x + 1 as a varies from 0 to 1. S Submit answer Next item Answers…

A: The problem is asking us to find the arc length of the function y = 5x + 1 as x varies from 0 to 1.…

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Q: Match each curve to one of the vector functions below. Possible vector functions: 1. r (t) =…

A: Step 1:Curve A is a circle when projected to the xy plane. But it exhibits sinusoidal variation in…

Q: 2. f(x) = x³-3x² +4 Find all relative extrema, inflection point, and the intervals of concavity 5 3.…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: 25 Given the following graph of the function y = f(x) and n = 6, answer the following questions…

A: Let's work through the solution step-by-step for estimating the area under the curve using both the…

Q: Please help me with these questions. I am not understanding what to do . Thank you

A: 1. Givenf(x)=x4+1x4​We have the following relation1+x1​=n=0∑∞​(−1)nxnSubstituting x4 in the place of…

Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: Find the value c in the interval [a, b] given by the mean value theorem for the function f(x) =…

A: Equation of the tangent line Graph