(2) Find the integrals: x² 2 • S √36x² dx

Q: The area of the surface formed by revolving the curve x = 2√1-y in the interval 0 ≤ y ≤ 1 about the…

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Q: Praw the curve r= 4 + 8 case and find the area outside the inner loop of the curve

A: Given: r=4+8cosθ

Q: (4) Recall the formulac: (5) Find the integrals: • ftan² (x) dx t: Is ta SC

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Q: 76°F Partly sunny -6-5-4 -3-2 y range 6 5 4 X = 3 2 1 (a) Find h(-2), h(0), h(2), and h(3). h(-2) =…

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Q: If f(x) = 1 - log5 x, then f-¹(x) =

A: Given that f(x)=1-log5 x , then our aim is to find the value of f-1 (x)=?

Q: Two fire-lookout stations are 14 miles apart, with station B directly east of station A. Both…

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Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

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Q: Mammator Mbaye ) Find the derivative of the expression - carefully. Do not simplify. (81) - 24r + 22…

A: To find out the derivative.

Q: 1 cos³x -dx =

A: The given integral is 1/Cos3x.

Q: Find the exact arclength of y = 2x3 for 0≤ x ≤ 2:

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Q: Find the linear approximation to f(x, y) f(6.11, 4.17) f(6.11, 4.17) = 5, xy at the point (6, 4,…

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Q: The slope of the tangent line to √x+y+√√xy = 2y at the point (2,2) is:

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Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 300…

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Q: CALCULATE THE AREA BETWEEN THE GIVEN FUNCTIONS. DEVELOP THE PROBLEM WITH ALL STEP EXPLAINED AND…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: Evaluate the definite integral: 0.8 4ze-2%dz = -0.2

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Q: Set-up the double integral that will solve for the volume of the solid in the first octant bounded…

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Q: 2).  Suppose that  ∞ n = 0 an(x + 4)n  converges at  x = −5.  At which of the following points…

A: Given that, the series is ∑n=0∞anx+4n, the series converges at x=-5. Rewrite the∑n=0∞anx+4n as…

Q: 1 cot³ x dx =

A: To solve the given integral.

Q: 1. T 3 x² - 2x + 6 (x² + 2)(x − 2) dx

A:

Q: Find the derivative of the function f(x) = e8+5x³. O f'(x) = 8+52³ O f'(x) = (8 +5x³) e³+5x³ O f'(x)…

A: To find derivative f'(x)

Q: Find the volume V of the solid of revolution that results when the region under the graph of f(x) =…

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Q: e Find the volume generated by revolving the area enclosed by the loop of the curve y² = x (x-3)²…

A: Solution is given below:

Q: Evaluate the following limits if they exist: lim In (3x-1) 5+x x->-5 e a) b) x-lnx lim x-e* lnx-1 El

A: limx→-5ln3x-1e5+x

Q: fa¹e² da dx: Applying the integration by parts technique, let Consider the integral Ա 4 X dv = ex x¹…

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Q: 8. Integrate the following definite integrals. Express answers in exact form (no decimal fractions):…

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Q: Consider the region R bounded by the functions f(x)=3x and g(x)=x²+2. The area of R is: Choices: sq.…

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Q: 3. S (5x-12)dx x3-6x²+8x

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Q: 2 y²dx + xydy = 0

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Q: ) In the following exercises, use direct substitution to show that each limit leads to the…

A: The objective of the question is determine the limits of the given function.

Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors 1² +2 x² +2…

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Q: If [ 2013 |檳 sin ada = −a³ cos x + 3x² sin x + k fæ sin ædæ, find k d. 3/2 a. 6 b. -3/2 C. -6

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Q: ● ftan(x) sec(x) dx

A: We will use substitute method to solve the integration

Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors x+8 x+8 x²+x-2…

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Q: (5) Find the integrals: •ftan²(x) dx ● fsec²(x) dx • ftan³(x) dx ●

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Q: If z² - 3yz² + xyz -2=0, find Az дz and дх ду

A: The objective is to find the Partial derivatives.

Q: r³+3x+1 8) (x+1)²(x-2)²

A: The objective of the question is determine the partial fraction decomposition. Note -  As per our…

Q: 6. If a = 2, b = 2√√3,7 = 30°, solve for c and 3.

A: We know that cosine rule is c=a2+b2-2abcosγGiven data a=2, b=23 and γ=30c=22+(23)2-2*2*23*cos(30)…

Q: Find the lengths of the functions of x over the given interval. Approximate if necessary. y=e^x on…

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Q: S= dx 3+ sinx+cos X

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Q: If ¹f [ 2³ sin ædæ = −2³ cos x + 3x² sin æ+ 6x cos a - 6 [ f(x)dæ, then f(x) = a. x cos x b. sin x…

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Q: what does the following integral equal? L 9(2)dz - [ = ['s g(z)dz = 23 and g(z)dz = 6.5

A: Given:             ∫-9-1gzdz=23              ∫-4-1gzdz=6.5              ∫-1-4gzdz=-∫-4-1gzdz

Q: Find the average rate of change of f(x)=ln(x)fx=lnx over the interval [20.25,39.5].20.25,39.5. Round…

A: The average rate of change of f(x)=ln(x) over the interval [20.25,39.5]

Q: car rental companies. Cars R Us charges $100 up front, plus 10 cents per mile. Thrifty Car Rentals…

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Q: A smooth curve C is defined by some vector function R(t) with R (7) 2 = = (π,0,−2) and R' (t) = (2,…

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Q: PRACTICE ANOTHER The graph shows the depth of water W in a reservoir over a one-year period as a…

A: Topic- Average rate of change of function over interval

Q: Use the Ratio Test to determine whether the series is convergent or divergent. 00 Σ n = 1 Identify…

A: To use the ratio test so that we can determine the convergent and divergent of the given series.

Q: Use logarithmic differentiation to determine I√I+1 (x+2)(x³+1) Y L2 7 2√2 O_7√2 72 3 at x = 1 for…

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Q: Which of these equations represents a line that is perpendicular to the line in the graph below?

A: Two lines are perpendicular if the product of their slopes is equal to -1

Q: 25. The vector field F(x, y, z) = (2xy + tan x)i + (x²-√y² - 1)j is conservative. a) True b) False

A: To determine whether the following statement is True or False.The vector field F→x, y, z=2xy+tan…