Evaluate the limits using the L'Hopital's Rule. lim (tan x) (sin x-1) x+2+

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: The height of a ball launched in the air t seconds after it is launched is given by:…

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Q: Let f(x, y) = (x³ − x)(y² – 1). Find fry(x, y).

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Q: Solve the linear ODE using an Integrating Factor. dy dx - 3y = 8e5x

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Q: 3. Find f'(x) if f(x)= 3 2x + sin r

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Q: Given that sin(0)= TT 3 and 2 <0<π what is the exact value of cos(20)?

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

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Q: What is the volume in cubic units of the solid formed when the region bounded by x = y - y^2 and x =…

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Q: I f 1 1-y Evaluate O a. 16 946 O b. 16 936 O c. 8 945 O d. None of the choices. O e. 16 945 xy₁√//1-…

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Q: B. Find the derivative of each of the following functions. 14. f(x) = x² + 5 3x + 2

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Q: Volume of Solid of Revolution Problem Revolve about the (a) x-axis and (b) y-axis the area enclosed…

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Q: A manufacturer needs to make a cylindrical can that will hold 1.5 liters of liquid. Determine at…

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Q: Let S be the collection of points (x, y, z) that satisfies all of the following inequalities: 0 ≤ x…

A: Here Z is function of x and y so first we have to integrate w.r.t z then x and y.

Q: 1. f³₂ (x² − 3) dx -2

A: Given :∫-23x2-3dx

Q: EX 3! Show that F (x₁y) = (2xy - 3) + " + (2y + x² ) 5* is conservative and find a potential of it..

A: Use the partial derivative for finding the potential function

Q: ƒ sin (3x³) dx

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Q: 2. Find the interval of convergence of the power series & 3x गय

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Q: 9. ✓ (at x = ()) (at x=-2) 10. ✓ 2 (for all values of x) (at x = 3) 8.

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Q: Using the Law of Sines to find a triangle with one obtuse angle if ZA = 50°, a= 23, b = 25. If no…

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Q: 1. Use Comparison Test to determine the converges or diverges of the series Σ: 8 n=1 (n+1)√n

A: By using Comparison Test to determine the convergence or divergence of the series ∑n=1∞ 1n+1n.

Q: What is the exact value of sin(67.5°)cos(22.5°)?

A: Solution-

Q: 1. -3 Given that 9+x² following functions: (−1)n+1 Σn=0 32n+1 1. f(x) = 5 arctan x2n. Obtain the…

A: We have to obtain power series representation.

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 6x2 + 6y2, where x…

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Q: Use double integration to find the volume of the solid on the first octant enclosed by the curves x²…

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Q: (5x)" . Given the power series Σ(-1)", , find and justify its interval of 4n In(n)' n=2 onvergence…

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Q: III. In each of the following, express the required series in summation notation. TL 2. Find the…

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Q: Let f(x,y) = 8x - 2y + 5. Find the following values of f(x,y) for the given coordinates. (a) f(2,…

A: Given  f(x,y)=8x-2y+5 Find:f(2,-1) Substituting x=2 and y=-1 in the given equation, we get  f(2,…

Q: Evaluate the multiple integral. * 131-x² SS S dz dy dx 100 0 2/3 5/3 4/3

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Q: 1. A farmer wants to fence in a field and divide it into four side by side, equal areas. If he wants…

A: From the given data And, xy=8000&amp;f(x,y)=2x+5y is the parimeter to minimize.

Q: Find fx (x,y) and f, (x,y). Then, find fx(1, -2) and fy (-3,3). f(x,y) = -2xy +9y² + 10 fx(x,y)=

A: We can find the answer as below.

Q: Compute the effective rate of interest corresponding to a nominal rate of 4.8% compounded…

A: We need to use effective interest formula.

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

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Q: 2. A particle is moving along an s-axis, where s is in feet. During the first 5 seconds of motion,…

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Q: Evaluate the following limit lim (3¹6) (²-√²+₂) Ꮳ X-4 -64 Show all your work. Warning: You will get…

A: Limits

Q: 3. Find the area bounded by a parabola and any right chord (use the parabola y2 = 4ax, chord x = x₁)…

A: In this question, we want to find the area bounded by the parabola and a right chord.

Q: You deposit $2000 in an account with 3% annual compound interest. Complete the following, assuming…

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Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A: Using derivative

Q: 3. Σ7ne-² (Integral Test) n=1

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Q: Derive implicitly—Implicit differentiation. Please show a detailed solution. Also, comprehensive and…

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Q: Com A real estate firm estimates that the value of a certain property will be given by the function…

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Q: 1. ļ | sinh 3x dx

A: The objective is to evaluate the integrarion.

Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

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Q: Which of the following expressions gives the length of the curve defined by R(t) = tij +In tk…

A: We have to find arc length expression for the given vector function.

Q: Question 138 of 190 FINAL-Mathematics Temperatures in degrees Celsius (C) may be changed to degrees…

A: A detailed solution is given below.

Q: Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to comput derivatives. a. h'(2) b. p'(1)…

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Q: 5. Find the telescoping sum 2 k=3(k+1)(k-2)

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Q: Convert the rectangular equation x2 = −2y2 + 5x2 y2 to polar equation

A: The rectangular equation is x2=-2y2+5x2y2

Q: Evaluate efffxv xdv,where D is the tetrahedron with vertices (0,0,0), (2,0,0), (0,2,0) and (0,0,2).

A: Given problem:- Evaluate  ∫∫∫D xdv ,where D is the tetrahedron with vertices (0,0,0), (2,0,0),…

Q: Suppose that x units of one input and y units of a second input result in P = 55x + 65y = x² - y² -…

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Q: Given that Inx+3 f(x) = 3lnx-1 Find the formula for f−¹(x). State the domain of f−¹(x). Show all…

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