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Q: Calculus Question

A: Given Data The equation of a parabola from 0 to 2 is y=x². The equation of a parabola from 0 to 5 is...

Q: Which of these is the unit vector in the direction of (1, 2, 2) ? A) (1/3, 2/3, 2/3) 2 2 V5' V5 С) (...

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Q: Find the indicated partial derivative. f(x, y) = xe−y + 4y; ∂f ∂y (1, 0) ∂f ∂y ...

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Q: Find the general solution of the first-order linear differential equation. dy + 9y = 27 dx %3D

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Q: Find the average distance from a point P(x, y) in the disk x2 + y2<=a2 to the origin.

A: Average distance is given as

Q: Supply the details for the proof of the Weierstrass M-Test (Corollary 6.4.5).

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Q: Suppose the curve y = f(x) passes through the origin and the point (1,1). Find the value of the inte...

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Q: EXAMPLE 4 Line integral of a conservative vector field Evaluate |(2ry – z) i + (x² + 2z) j + (2y – 2...

A: The line integral of a conservative vector field is C is a simple curve from A(-3,-2,-1) to B(1,2,...

Q: Use the Ratio Test to determine whether the series converges.

A: To determine the convergence of series.

Q: Consider the following problem: A farmer with 750 ft offencing wants to enclose a rectangular area a...

A: Given that, The fencing encloses a rectangular area is 750 ft. The rectangle divides it into four pe...

Q: at what x-value does the function y=cot (x) have a vertical asymptotes?

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Q: Find the area under y = x3 over [0, 1] using the followingparametrizations. x = t2, y = t6

A: Consider the given equation and parametric equations

Q: A cone-shaped tank with the tip down has a radius of 10 ?? and a height of 20 ??. We lead water into...

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Q: The revenue for a certain product is given by the equation R(x)=100−400x+5−x, where x is the number ...

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Q: Use separation of variables to find the general solution of the differential equation. dr 0.03r ds

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Q: indicate a good method for evaluating the integral (but do not evaluate). Your choices are: substitu...

A: Given: To Show: A good method to solve the above integral from the choice: Substitution Method Inte...

Q: Could you help me with this question? I'm not sure how to solve for the values. I'd appreciate the h...

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Q: Find general solutions of the differential equation xy'=y+2(xy)^1/2

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Q: Solve the given differential equation by separation of variables. dy = x1- y?

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s). f...

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Q: Find the exact length of the curve. x= 2+ 92 y =4+ 6 Osts5

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Q: determine whether it diverges or converges. If it converges, find the value of the integral

A: To determine if the integral is convergent or divergent.

Q: Calculate the derivative at the point (0,0) of the function given by the equation x=y−2siny.

A: Differentiating with respect to x, we get

Q: Calculus Question

A: Given a=1.41 , b=2.01 , C=51.9 degree

Q: Use integration to find a general solution of the differential equation. (Use C for the constant of ...

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Q: Conservative fields Use Stokes’ Theorem to find the circulationof the following vector field around ...

A: Given: F = ⟨y2z3, 2xyz3, 3xy2z2⟩ To Find: Circulation of the F around any simple closed smooth curve...

Q: The following series are geometric series or a sum of two geometric series. Determine whether each s...

A: ----------------------------------------------------------------------------------------------------...

Q: (d) The open intervals on which f is concave downward. (Enter your answer using interval notation.) ...

A: If the function faces downwards then it will be concave down So the function is concave down in (0,...

Q: Use the graph of the greatest integer function y =⌊x⌋

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Q: Show that 13x - 12 can be made as small as desired by taking x close to 4. lim(5x + 2) = 17x➔3

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Q: compute the definite integral.

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Q: Which matrix C is defined? Explain why! b. Calculate the product from problem (a) where ...

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Q: Graph the functions. What symmetries, if any,do the graphs have? Specify the intervals over which th...

A: Given: The following graph is drawn for the given function,

Q: Solve for y in two ways. y' - 5y = -3

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Q: Show that the function y=e−2x(sin3x+cos3x) is a solution of the differential equation y′′+4y′+13y=0.

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Q: Find ds/dt when θ = 3π/2 if s = cos θ and dθ/dt = 5.

A: Differentiating with respect to t, we get

Q: Let P(x0, y0) be an arbitrary point on the graph of f that f′(x0) ≠ 0, as shown in the figure. Verif...

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Q: Find an antiderivative of the function f(x)=e2x.

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Q: Find an equation for the hyperbola with foci (0, ±10) and with asymptotes y: = +x.

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Q: Find the values of the function. f(x, y, z) = x y − z (a) f(15, 2, −2) (b) f(8,...

A: Answer(a):

Q: Find the limit.

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Q: Find the most general antiderivative of the function.(Check your answer by differentiation.) f ( x...

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Q: Let a curve be parameterized by x = t³ – 9t, y =t+3 for 1< t< 2. Set up (but do not evaluate) the te...

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Q: Use sigma notation to write the sum.

A: Here,

Q: Complete the table by finding the appropriate logarithmic or exponential form of the equation, as in...

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Q: I will appreciate detailed explanation with short comments, so I can do similar exercises.

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Q: Use logarithmic and exponential integration rules to evaluate the following integral.

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Q: Solve the equation dy /dx = k y

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Q: Evaluate the trigonometric function. Round your answers to four decimal places cos(−3/7 )

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Q: Suppose in 2020 you have $13800 in an account earning 0.8% annually. How much money will you have in...

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Transcribed Image Text

Prove that the volume of a segment of height h of a sphere of radius r is V = }nh°(3r – h)