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Q: √3 + √75 = √3 +√25 . 3 = √3 +_______ √3 =_______.

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Q: Find the derivative of the inverse function for y=x3−3x and calculate its value at x=−2.

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Q: Use the initial condition to find the particular solution of the differential equation. dy = 4xy sin...

A: In the given question apply the variable separable method, i.e, isolate the y terms on the left side...

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: In Problems 31 through 42, verify that the given differential equation is exact; then solve it. 38. ...

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

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Q: Calculus Question

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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: Greatest integer function Find (a) lim, 400 [x] and (b) lim, 400- (x ); then use limit definitions t...

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Q: please explain and show all parts

A: Given integral is,

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:

A: Given:

Q: - e d山 e +e==

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Q: The total cost to manufacture and sell q exactotherms is given by the cost equation C(q) = 2000+5q. ...

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Q: Calculus Question

A: Given:

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

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Q: The equation for the moment about the origin of a one-dimensional system is M0 = 5(−3) + 2(−1) + 1(1...

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Q: Investment The rate of growth of an investment is proportional to the amount in the investment at an...

A: The rate of growth of an investment is proportional to the amount in the investment at any time t. ...

Q: Investigate the one-sided limits graphically: (a) lim x→2# x – 2 (b) lim x→0± x2 (c) lim In x x→0+

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Q: Solve each equation for y and then determine whether the equation defines y as a function of x: a. 2...

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Q: Find the limits. Write ∞ or -∞ where appropriate. limx2 - 3x + 2/x3 - 4xas x→1+

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Q: Find the area bounded by f(x) = -x² +4x +1 and g(x) =x+1

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Q: Evalucte the following Integal ん +e-)し ーうL n -E dy. e te 4 sm (4nt$) dn

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Q: Simplify exponential expression. 7x5y6 / 28x15y-2

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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: Find the derivative of f(x) = ln(2x^3 + x).

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Q: Limits at InfinityFind the limits in Exercises 41–54.

A: Dear student, Since you have posted multiple questions, as per our policy we will answer first quest...

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: use a triple integral to find the volume of the solid bounded by the graphs of the equations . z = 8...

A: Given

Q: Find the volume of the solid generated by revolving the specified region about the given line. R3 ab...

A: The volume of the solid formed by revolving function f(x) along the line y = x can be found using fo...

Q: Estimate the slope of the tangent line at the point indicated. f(x) = lnx; x = 3

A: Slope of the tangent line is the derivative of the given function at the given point. So differentia...

Q: Use the given graph of f over the interval (0, 7) to find the following. (a) The open intervals on w...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: find dy/dt. y = sec2 πt

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Q: Use Hooke’s Law to determine the work done by the variable force in the spring problem. Six joules o...

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Q: Show that the polar equation r = a sin θ + b cos θ where ab ≠ 0 represents a circle, and find its...

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Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at ( 1 , 0 ) and endin...

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Q: please explain and show all parts

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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: 1 One-to-One Function? Determine whether the func- tion is one-to-one. 22. r(t) = * - 1 23. (1) - 4 ...

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Q: 17. Emptying a tank A vertical right-circular cylindrical tank measures 30 ft high and 20 ft in diam...

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Q: Find the acute angle between the planes x + y = 1 and y + z = 1.

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

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

A: Given

Q: Verify the solution of the differential equation. (Enter your answers in terms of x and C only.) Sol...

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Q: A bowl is in the shape of the graph of z = x2 + y2 from z = 0 to z = 10 in. You plan to calibrate th...

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Q: Evaluate the integrals:

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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: Which of these vectors is perpendicular to (1, 2, 3) ?MARK ALL THAT APPLY PLEASE. A) (–1, –1, 1) B) ...

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Q: Find the derivatives of the functions y = (9x2 - 6x + 2)ex3

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Q: Calculus Question

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question s...

Transcribed Image Text

53. Sketch the region under the graph of f(x) = 1+x2 for -00 < x < 00, and show that its area is I.