Example 1: z=x³y_x=2t and y=t² Find dz dt

Q: Using: Higher order linear equation with constant coefficent / Homogenous Please Solve this equation…

A: The given equation is a third order linear differential equation with constant coefficients. The…

Q: Use the given information to find the exact function value. Simplify your answer as much as possible…

A: Given that the expression

Q: 42. Integrate (7x³ + 4x²) dx. a. b. C. 7x+4x+C 7x+4x²+C 3 C. 3 3 7x3 d. 4 3 7x+4x+C 3

A: Since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: Let ā = (-1, -2, 2) and 6 = (0, 4, −4). Find the angle between the vector (in radians)

A: To find the angle between two vectors a→ and b, we can use the…

Q: Instructions: Sketch the graphs of the following functions. Write neat solutions. Make sure each…

A: As per our guidelines we can answer only 3 sub parts of the given question so kindly repost the…

Q: Rewrite the following iterated integral in the order dy dx dz: f(x, y, z) dz dy dx.

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Q: Differentiate the following. Simplify your answers. y = esin x tan x y=x465x-3 y =

A: To differentiate the following.

Q: #7 Given f(x,y) = x³y-xy-2x. find and classify (min, maxer saddle) all critical points.

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Q: Let w = xy − 3yz + xz, x = st, y = e³t, z = t² - Compute მი -(—2, 2) : = მs მო -(-2, 2): = at

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Q: I need help with this problem and an explanation for the solution described below (Discrete…

A: The objective of the question is to determine the truth value of the statement 'If 9 is not prime…

Q: Use a linear approximation (or differentials) to estimate the given number. e-0.01 Need Help? Master…

A: Given that  consider the function Linear approximation of f(x) about the point x=a is given by now,…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

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Q: 5 A polar curve is given by r = (3-cos(e)) What angle corresponds to the point on the curve with an…

A: Hence the final answer is : θ≈2.42,3.86 Explanation:To find the angle θ corresponding to the point…

Q: se z = x² sin y, x = 1s² + 1t², y = -6st. the chain rule to find oz and as function: as Əz d the…

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Q: 1. f(x) = (4x2)5

A: As per company guidelines for a question posted we are allowed to solve only first three subparts…

Q: I need help with this problem and an explanation for the solution described below (Discrete…

A: The objective of the question is to identify which of the given statements is a proposition. A…

Q: Consider how the methods of undetermined coefficients and variation of parameters can be combined to…

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Q: Please help me with this, thanks!

A: The objective of this question is to find the dimensions of the garden that will maximize the…

Q: Evaluate the integral

A: 1.  3(arctanx)3​+C2.  earcsinx+CExplanation:

Q: Find the area of the region lying between the loops of =2+4sine. Select one: ○ a. 4(√3+2π) O b.…

A: The area is:A=4(33​+π) The answer is d.Explanation:The given polar function is:r=2+4sinθFirst, let…

Q: Find the linear approximation to the equation f(x,y) = 2√ xy at the point (2,8,4), and use it to…

A: Therefore, the linear approximation to f(2.18,8.29)≈4.2525Explanation:Solution:-

Q: Use the formula for the sum of the first n integers to evaluate the sum given below. 3+ 6+ 9 + 12 +…

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Q: Find the exact length of the curve. x = et - t, y = 4et/2, 0 ≤ t≤ 3

A: the exact length of the given curve is(e3+2)Explanation:Please ask if you gets any doubtplease give…

Q: An investment of $10,000 earns interest at an annual rate of 6.7% compounded continuously. Find the…

A: $716.43 per year $900.55 per yearExplanation:To find the instantaneous rate of change in the amount…

Q: Find two unit vectors orthogonal to both = (2, -3, -2) and = (0, 5, 6). Give exact values (no…

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Q: A rectangular swimming pool is designed to be 7 times longer than it is wide. The total surface area…

A: Solution of the above mentioned problem is provided below for further queries u may ask in comments…

Q: 4. Below is the graph of f(x 10 2 " -5 0 5. -10- -20- 20 a. Find f'(x) FA-12x²-6x-2 b. Identify the…

A: The given function equation is

Q: 6 x = x= Find the point of intersection for the lines v(t) = (−7, −7, −9)t + (−3, 1, 3) and w(u) =…

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Q: Find dy dx if y = √Inx +1. 1 dy dx 2 x √In(x)

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Q: The resale value R (in dollars) of a particular type of laser cutting tool t years after its initial…

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Q: Website Profit You operate a gaming website, www.mudbeast.net, where users must pay a small fee to…

A: explained below Explanation:Step 1:(a) Construct a linear demand function for your website and hence…

Q: Find a Cartesian equation for the curve and graph the equation. r = 6 cos 0

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Q: Given 6 = 41 - 2j and d = -101 + 73, find 16+d| and |b|+|d|.

A: Given b→=4i→−2j→ and d→=−10i→+7j→.To find : |b→+d→|,|b→|+|d→|

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time interval…

A: Given that the a particle with position  as t varies,

Q: Exercise: Solve the equation d³y dx3 +3d²y dx² dx +30 + y = 0

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Q: 3) Evaluate the integral 00 a) √2° 1 x√√x²-4 dx b) S√ dx -1 x2-2x Π 4 xsinx c) Số cos3x dx

A: 3.a)

Q: (f'(x))² = 4 (52 – 8) - 25 = 20x 32 (f'(x))2 into the surface area equation above to find Surface…

A: To show

Q: Find the horizontal and vertical asymptotes of the curve. You may want to use a graphing calculator…

A: x = -1, 0, 1y = -1Explanation:Step 1: Write the numerator and denominator of the rational function…

Q: Complete the parametric equations of the line through the points (7,-7,-1) and (4,-4,8) x(t) = 7 –…

A: Solution is following in explanation step.

Q: On what interval(s) is the function g(x) = e notation.) (0.7) -8x7 both decreasing and concave down?…

A: We need to find an interval where the function is decreasing and concave down.

Q: A graph consists of the line y = 5 for 1≤x≤5 and y = -1 for-3 ≤x≤ 1. Find the accumulation of change…

A: A graph consists of the line .To find the accumulation of change under the curve from  by using…

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

A: The given parametric equation is: Use a graphing utility to graph the curve represented by the…

Q: Evaluate the indefinite integral. 4 ln(5 - x) dx √ 4

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Q: (a) Domain of f(x). (b) r-intercepts and y-intercepts. (c) Vertical asymptotes and holes. (d)…

A: Here we have given a function: .

Q: 2. [6 pts.] Evaluate lim f(x) and lim f(x) for the function: f(x) xx (Hint: the limits will be…

A: Limit at infinity = 1 Limit at - infinity = 5Explanation:Step 1: Step 2: Step 3: Step 4:

Q: c) 18x-19 2x²-5x-3 dx

A: To evaluate the following integral.

Q: ax.)-( Find the centroid of the region shown, not by integration, but by locating the centroids of…

A: In the given region we have one rectangle and one triangle.Region 1 is rectangle and region 2 is…

Q: Find a rational function f that satisfies all the given properties vertical asymptote at x = 4 and…

A: The objective of this question is to find a rational function that has a vertical asymptote at x = 4…

Q: 5 ст The slope of the tangent line to the curve y = at the point 8, is: x 8 The equation of this…

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Q: Solve the given initial-value problem. x²y" + xy' + y = 0, y(1) = 1, y'(1) = 5 y(x) = , X > O Use a…

A: The given differential equation