Find dx dt dy dt dy dx dx dy dt' dt || || dy dx x = 3t³ + 6t, || and y = 5t-4t²

Q: Use the graph to determine (a) open intervals on which the function is increasing, if any. open…

A: Where ever (i.e., for all x values) on the graph the function looks like a line parallel to x-axis…

Q: Pictured below are a contour map of f and a curve with equation g(x, y) = 8. Estimate the maximum…

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Q: дz Use the chain rule to find and მs əz əs 11 дz at Z = = (x - y)⁹, x = s²t, y = st²

A: The given function .Use the chain rule to find  and .

Q: Q4 Find the following integral. Show all your work. (2 si 2 sin (20) - 3eº 0³ +1 O√O +π. In (0))) 0…

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Q: Solve the given initial-value problem. y(x) = y" + 4y' + 5y = 35e-4x, y(0) = -6, y'(0) = 1

A: The solution is shown in step-2

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

A: Graph

Q: Approximate the area under the curve graphed below from x = 3 to x = 8 using a Left Endpoint…

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Q: Determine the global extreme values of the function ƒ (x, y) = x³ + x²y +9y² on x, y ≥ 0, x + y ≤ 4.…

A: The solution is shown in step-2

Q: Find the area of the shaded region below. Area = x=y²-2 y=-1 YA y = 1 x = ex x

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Q: Evaluate the integral. [* (7 +³1 (7t³/²i + (t + 8) √tk) dt

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

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Q: plume of the solid obtained by rotating the region bounded by the curve x²+(y-1)²=1 about the…

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Q: O Find the to Nowings trignometric integrations dx (sin23 Scos x S

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 3. Intersections. Find the six intersections of the following two parametric curves. Give exact…

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Q: 4x - 2y -d.A, where R is the parallelogram enclosed by the lines ° R-5x - 4y Find 4x - 2y =0, 4x -…

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Q: (Secx ) 4 (tan x)² dx.

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Q: 35-38 Use the binomial series to expand the given function as a power series. State the radius of…

A: The solution is shown in step-2

Q: Given f(x, y) = -2x³ – 5xy² + y^, find the following numerical values: fx(2,3)= fy(2, 3) =

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Q: Given that 3 is a zero of the polynomial function f(x), find the remaining zeros. (x)=x³-5x² +23x-51…

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Q: Use a parameterization to find the flux SSF-n do of F= 4xy i - z k outward (normal away from the…

A: The solution is shown in step-2

Q: 4. Use implicit differentiation to find the equation of the tangent line to z²+zy + y² = 3 at the…

A: The slope of the tangent line to the given curve is equal to the derivative of the given function at…

Q: Use the Limit Comparison Test to determine if the following series converges or diverges. 00 1 Hint:…

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Q: n -1+n* converges. 1+² Use the limit comparison test to determine if n=1 Compare to n=1

A: The given series is

Q: Please show work and all steps clearly. Thank you. Find the volume of the solid obtained by rotating…

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Q: Find an equation for the tangent to the curve at the given point. 7. f(x) == 6 square root of x - x…

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Q: Evaluate lim x 0 cos(x+2) sin x Show all work.

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Q: Find the area of the ellipse cut from the plane z = 9x by the cylinder x² + y² = 16.

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Q: A table of values for f, g, f', and g'is given. f(x) g(x) 3 2 x 1 2 3 ليا 1 7 8 2 (a) If h(x) =…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: The current in an electrical circuit is given by the formula I = the time, in seconds. t+2 15-t'…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Given f(x, y) = 2x³ – 3xy – y³, find fxx(x, y) = fay(x, y) =

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Q: Q1.8 b If f* f (2) dx = [*9(2) de a True False g(x) dx = 5, then S* (f(x) + g( a (f(x) + g(x)) dx =…

A: (Given)"Note that as per the rules, we are supposed to answer the first question as these are the…

Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

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Q: Solve the given differential equation by undetermined coefficients. y" + 5y' + 4y = 12 y(x) =

A: The solution is shown in step-2

Q: Solve the given differential equation by undetermined coefficients. y"-y'- + y(x) = y = = 7+ex/2

A: The solution is shown in step-2

Q: Consider the region R bounded by the line y = 47 - 9x and the parabola y = 27 — x². - To find the…

A: By the answering guidelines of Bartleby, We can answer only question from multiple questions, please…

Q: r +3 lim- 7-9 √√T-9 V

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Q: The average cost of a product changes at the rate C '(x) = −8x−2 + 1/8 and the average cost of 8…

A: Given that, the average cost of a product changes at the rate of  and the average cost of the 8…

Q: 8 2. Consider the power series: Σ(3x - 1)^. n=0 ● Identify the center of the power series. Determine…

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Q: Find the equation of the tangent line to the graph of the function f(x) = (1,−14). (x²+6) (x − 3) at…

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Q: Find the particular solution to the differential equation. x²e4y dy = (x³ + 2) dx when x = 2, y = 0…

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

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Q: Determine all the points where the given function is continuous 4 f(x,y)=√. y²+z²-4 a. x² + y² +2²4…

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Q: 37. f (√x + √√xª) dx - 39. √5²|x − 3 | dx 41. ², (x - 2|x) dx 38. f'(1 + x²)³ dx 40. ²|2x - 1| dx…

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Q: For each value below, enter the number correct to four decimal places. Suppose an arrow is shot…

A: Height To findaverage velocity

Q: Use a graphing utility to graph the curve represented by the parametric equations. Indicate the…

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Q: Find the critical points of f. Assume a is a constant. 1 13 12 = -√3x¹3 - a¹²x 13 f(x):

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Q: Find the arc length L of the graph of r(t). r(t) = t³ i + 1 j + ½ √61² L = i k, √61² k₂ 3 ≤1 ≤4

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Q: Find the derivative of the function. f(t) = sin²(esin²(t))

A: The Power Rule:The Chain Rule:

Q: mon κ k=1 vk3 + 4k + 3 15. Σ

A: Use the limit comparison test