Determine the inverse Laplace transform: F(s) = (5 - 2s)/(s2 + 7s + 10)

Q: Evaluate the following integral, (9x - y²)dx + xy dy where C is given by x X = 5t, y = √t, 0 ≤ t s…

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Q: If C(x) is the cost of manufacturing an amount x of a given product and $10 is the price per unit…

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Q: If z² = x² + y² with z > 0, dx/dt = 2, and dy/dt = 6, find dz/dt when x = 6 and y = 8. dz dt Answer:…

A: The Power Rule:The Chain Rule:

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A: Absolute maxima :Absolute maximum is the highest point or value of a function within its entire…

Q: A large tank is partially filled with 150 gallons of pure water. Brine containing 2 pounds of salt…

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Q: Evaluate the indefinite integral. +C 5- 4 sin x Cos x dx

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Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. dy dx…

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Q: Find the direction cosines and angles of u and show that cos²a + cos² ß + cos² y = 1. (Round your…

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Q: To test this series for convergence ∞ n=1 n n6 + 7 You could use the Limit Comparison Test,…

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Q: 4. COS V sin v = csc v sin v 5. cot(a) cos(-a) + sin(- α) - csc (α)

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Q: Find the indicated trapezoid approximations to the following integral. 18 [9x² 9x dx using n = 2, 4,…

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Q: 140 -x³ to answer the questions below. 3 3 747x4 tical numbers of f(x)? x = - l(s) is f(x)…

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Q: Suppose f (x, y) =x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

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Q: Use Rolle's Theorem and a proof by contradiction to show that the function f(x) = 6x³ + 4x - 11 does…

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Q: For the given double integral, sketch the region of integration and write an equivalent double…

A: For the given double integral, to sketch the region of integration and to wrire an equivalent double…

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4 + x² -…

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Q: Consider g(t) = 3t+ 6t² - 1 + 6t³+2+¹ Determine the intervals on which g is concave down. g is…

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Q: Find the lines that are tangent to the curve y=2tan(pi*x/2) at x=1

A: The equation of tangent line passes through point  with slope

Q: For which value of t does the line given by the parametric equations x=t-1, y = 1+ 2t, z = 3-t pass…

A: x=t-1y=1+2tz=3-tPoint (-2,-1,4)

Q: For each of the described curves, decide if the curve would be more easily given by a polar equation…

A: The equation of a line through the origin that makes an angle a with the positive x-axis is  = aThe…

Q: Let 16x-5 1x² +5 Enter the exact value of the one-sided limit lim f(x) 3-2 f(x) = if x ≤ 2 if x > 2

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Q: If the governing equation is do + 1 = g(t), what is the solution g 20 dť² when g(6)=0 and when g(t)…

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Q: Step 3 Write the two binomial factors so that the first term of each factor is x and the second…

A: To write the complete factorization of

Q: Let f(v) = v +17 v + 12 Determine the critical values of f. Write exact answers. Do not round off.…

A: Given,

Q: SYSTEM: x + y + z = 6 2x - y + z = 3 3x z = 0 -

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Q: For this interval notation, draw its graph and write its equality: (-∞0, 6]

A: The given interval is .The aim is to sketch the interval and write its equality.

Q: Use upper and lower sums to approximate the area of the region using the given number of…

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 2xe…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 12 + 2x -…

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Q: Consider the function graphed to the right. Make sure to use the union symbol, U if needed. The…

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Q: 2. Use Calculus to find all local extrema of the function g(x)=x√3-x.

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Q: The graph of y = f(x) is given below. -5 150 num -4 lim f(x) AI-1 -3 -2 5 4 3 2 -1 -1/ 1 2 4…

A: A graph of the function  is given.The aim is to find the given limits.

Q: Evaluate the following integral, f (x - 5y) dx - 8y² dy where C' is given by x = y² + 6 from (7, 1)…

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Q: Consider the following. x = e-5t, y = e5t (a) Eliminate the parameter to find a Cartesian equation…

A: Consider the following.To eliminate the parameter to find a Cartesian equation of the curve.

Q: x³ (4x - 4)5 Let f(x) = 3x² - 3 If we use the method of logarithmic differentiation to find f'(x),…

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Q: Find the differ y = √3 dy= = Evaluate dy fc x = 1, G y =

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Q: If the functions f, g are linearly independent, then the functions f − g, f + g are linearly…

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Q: Solve the given initial-value problem. y(x) = 2y" + 3y - 2y = 10x² - 4x 13, y(0) = 0, y'(0) = 0 -

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

Q: 8. Consider the gradph of the function f(x, y) = x² - 5xy given by z = x² - 5xy (a) ( (1,2). Find an…

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: Find fx fy and f, and evaluate each at the given point. f(x, y, z) = xy x+y+z (3, 1,-1) fx(x, y, z)…

A: The given function is

Q: For every solution y(x) of the equation y''+ 2y'+ 5y = 0 it is true that limx→∞ y(x) = 0. ?

A: Consider the equation

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Assume that  are both  differentiable  functions of t.(a) To find , given that (b)  To find , given…

Q: find maximum rate of change of f(x,y)=x sin(y) @ the point (2,0)

A: To find the maximum rate of change of at the point .

Q: Suppose that P(t) (with t in months), the fish population in a lake contaminated by chemicals,…

A: Given Differential equation as follows

Q: If 1800 square centimeters of material is available to make a box with a square base and an open…

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Q: Form a polynomial whose real zeros and degree are given. Zeros: -4,0,3; degree: 3

A: Form a polynomial whose real zeros and degree are given.Zeros: -4,0,3; degree: 3

Q: lim √xe-x/2 x → 00

A: L=limx→∞xe−x/2

Q: = O Trigonometric Identities and Equations Proving an identity using fundamental trigonometric…

A: 1+tan2x