25 2=9. - Maximize Q=xy, where x and y are positive numbers such that x +- and y = The maximum value of Q is and occurs at x = (Type exact answers in simplified form.)

Q: Find the first three terms of Maclaurin series for F(x) = In (x+3)(x+3)²

A: A Maclaurin series is a special case of a Taylor series, obtained by putting x = 0 i.e.,

Q: Directions: Using Fundamental Theorem of Calculus (FTOC), compute the following definite integrals.…

A: Since you have posted a question with multiple sub-parts, as per company guidelines we will solve…

Q: Let f(u) = ³√u and g(x) = u = 2 + 12x². Find (fog)(1). (fog)'(1) = (Type an exact answer.)

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Q: Acceleration due to gravity in feet per squared second is the constant function a(t) = -32. Suppose…

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Q: Luate J 1+sin 1-sin 2 r da

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Q: Determine the intervals on which the graph of y = f(x) is concave up or concave down, and find the…

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Q: Find the maximum and minimum limits of the function f(x) = - X-2 (x+2)²

A: Given ,f(x)=x-2(x+2)2We know that ,Suppose that x=c is a critical point of fx then, If f 'x<0 to…

Q: Consider a right triangle with a side of length x opposite angle A, a side of length y opposite…

A: Consider a right triangle with a side of length x opposite angle A, a side of length y opposite…

Q: Solve the following system of inequalities 2x+y-8>0 3x-y+6>0

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Q: ) Write a MATLAB code for solving the following equation : N Y = [i+x i=1

A: MATLAB code

Q: Please kindly show all working. Thnx. 1) Let f(x)=x3−3x2−9x+25. Use the derivative…

A: Given function,f(x)=x3−3x2−9x+25.We know that.Suppose that x=c is a critical point of fx then, If f…

Q: Differentiate with respect to t. y = d cos(t) + t² sin(t) y'- sin d( 2t + d) + t²cos (t)

A: Given problem:- Differentiate with respect to t.   y = d cos(t) + t2 sin(t)

Q: The contact force therefore can be expressed as a a 27 F 2xÊ / ºr (d-1²) dr = -1°2xr 2xr Ozz dr n 2R…

A: We know that integration of xn is xn+1/n+1.     Here i attached the solution of this question.

Q: (a) What angle in radians is subtended by an arc 1.50 m long on the circumference of a circle of…

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Q: In2 fin² coshx dx

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Q: Apply the second derivative test to find all relative extrema. (c) f(x) = 1

A: To find the relative extrema first we  find the critical points. The critical points are the values…

Q: The equation N (t) = 500 = models the number of people in a town who have heard a rumor 1+49e-0.7t…

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Q: Solve: 123 1 224 + 1 315 - 4x6 +...? +

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Q: 2. What details are used in order to analyze the polynomial function and analyze to sketch the…

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Q: Find the critical points of the function f(x) = x³ + 1¹5 x² + 50x + 8. Use the First Derivative Test…

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Q: 1 5 X If y = - find dy dx at x = 2.

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Q: Show that if the function f(x, y) = ex siny + ecosx, satisfies Laplace Equation.

A: We can solve this as follows:

Q: 1 +x² √x (+/- + x² Given f(x)=x√x + x and g(x) - = f(x) (exe-1-x-3/4+) (² + x² g(x) √x)² 1 ° = [e…

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Q: Please fix the mistakes that are in Red for me.

A: Note: Since you have posted a question with multiple subparts we will solve the first three parts…

Q: Consider the following function: Step 2 of 3: Find f Answer f(x, y) = (4x + 3y)

A: I have stated the used formula and the property in the solution

Q: . Find the integral [cos (3x - 2)dx

A: A detailed solution is given below.

Q: Show that the equation is homogeneous and find its solution. (x2 + 3xy + y2) dx - x2 dy = 0

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Q: dy II. Use the Inverse Function Rule to find (show your complete solution) dx 1. x = y + y² + y³

A: Given

Q: Find the length of the curves in Exercises 1-4. x = (y³/2/3) - y¹/2 from y = 1 to y = 9

A: Solution of given question is written in below steps.

Q: f2₁ (4x + 5) dx

A: ∫-12 4x+5dx

Q: 2. (5 pts.) If f(x) = xºex, find f'(x) and f'(1).

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Q: Let f(x) = x²30 Find the critical points c that correspond to local minima.

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Q: 2. √√√x + y + xy = 21

A: We have to find out derivative

Q: ex V1-e2x 1. S dx

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Q: A ladder 25 ft long rests against a vertical wall. If the bottom of the ladder is sliding away at a…

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Q: explain using a graph of (x) = X³-6x, for 0≤x≤3 With Six sub intervals, what the Riemann sum…

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Q: Solution 1 y = (x +3)(2x – 5) y = 2x² + 6x - 5x - 15 y = 2x2 + x - 15 y = 2(2x)2−1+1-0 y' = 4x+1…

A: Please see the below picture for detailed solution.

Q: Is it possible to solve all the points with Finding Domain and Range 1) y sin x 2) y = cos x J= tan…

A: Solution is given below

Q: Q4) Find the maximum eigen value for the system 4 = x¹ (0) = (1 1) 3 12 54 with initial vector

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Q: Differentiate the function. y = (2x-5)³ (5-x4) 4 dy dx

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Q: 1. Evaluate the Riemann sum for (x) = x³ - 6x, for 0 ≤ x ≤ 3 with six subintervals, taking the…

A: We need to solve using Reimann sum.

Q: A sort of "decay" Suppose that newly-baked cupcakes are taken out of the oven which is set at 100…

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Q: Find the maximum and minimum limits of the function X-2 (x + 2)²

A: Explanation of the answer is as follows

Q: If z=x2sinh 4 then 02z дхду

A: Explanation of the answer is as follows

Q: Consider the function. 700----14 Identify the domain off. (Give your answer as an interval in the…

A: We need to fill answers.

Q: Forces of 19lbs and 40lbs act on a body producing a resulting force of 50lbs. What is the angle…

A: The given two forces are 19lbs and 40 lbs. The resulting force is 50 lbs. Because the resultant is…

Q: Approximate the value of In (1000!)

A: Here we have given ln1000!. Now finding it's value we get : As we know that expansion of lnx is…

Q: In t years, the population of a certain city grows from 500,000 to a size P given by P(t) = 500,000…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find an equation of the line tangent to the graph of f(x) = a) at (1,1); b) a (-37) at a) The…

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Q: 2xydx +(1+x²) dy

A: 2xydx+x2+1dy=0