What could be an integrating factor in solving the differential equation (1 +x*)+(1-x)y = xe* ? +(1– x) y = xe ?

Q: The height of a cone is decreasing at a constant rate of 3 centimeters per minute. The volume remain...

A: V=13πr2hSubstitute V=52 and r=6 into the above equation52=13π(6)2h h=52×336πh=133π cm

Q: Find the radius of convergence and the interval of convergence. Σ (k+3 k=0 Radius of convergence: In...

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Q: SS 2x dæ dy 0 < x < y³ and 0 <y<2 1 decimal

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Q: w.6 Fwe cars A +B move tersect at right angleftewards the intersection paint AL 25 mi/tr and 30 mi/h...

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Q: Given revenue and cost functions R(q) = 70q - 0.3q and C(q) = 14q + 500, find the quantity that maxi...

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Q: The cost of a can of Coca-Cola in 1960 was $0.10. The function that models the cost of a Coca-Cola b...

A: topic - exponential function

Q: emine whether the series is convegent or divergent. If it an=lo00,evaluate lim Can) Cos M8

A: We have to find the value of the given limit according to the given information

Q: interval leugth Y =9

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Q: The graph of y3f(x) is given. Solve the inequalities. Write the solution sets in interval notation i...

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Q: Given the function f(x) = (x+3)²(x-1). Find the critical points of f(x) and its increasing and decre...

A: f(x)=x+32x-1f'x=x+32ddxx-1+x-1ddxx+32       =x+32+2x-1x+3       =x+3x+3+2x-1      =x+33x+1to find cr...

Q: nAבencח x2 f(x) Let k(x) = %3D 2x- 3 Find k'(-1), given that f(-1) = -2, f'(-1) = –3. Sorry, that's ...

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Q: 15. Vlad and Karl discuss about the continuity of the given function. Vlad asserts that the function...

A: A function f(x) is said to be continuous at x=a iff limx→a-f(x)=limx→a+f(x)=f(a) A polynomial functi...

Q: Consider the function on the Interval (0, 2x). f(x) = 4 sin? x + 4 sin x (a) Find the open interval(...

A: We will have relative maxima when the derivative changes sign from positive to negative. And for rel...

Q: Convert the parametric equations of a curve into rectangular form. No sketch is necessary. = Vt, y =...

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Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an imprope...

A: First we take partial fraction , it is telescoping series. Follow step 2nd . 

Q: below. II imit does not exist or the functi1on is undefined, write DNE. бл3 + 10а? a. Consider h(x) ...

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Q: C. Find the values of the constants c and k that make the function continuous at every number. S3x +...

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Q: Determine whether the alternating series converges. k + 1 >(- 1)k+1 6k + 1 k=1 O The series diverges...

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Q: 24. Use Newton forward-difference formula and construct appropriate interpolating polynomial and app...

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Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answ...

A: gx=x2+4x23,  -7≤ x≤8

Q: Decompose the function y = (2-2x*)³ in the form y = f(u) and u = g(x). (Use g(x) = 2 – 2r*.) Provide...

A: In this question we have to find the value of x and y.

Q: of (x)} = h %3D a Find leughth

A: Length=integration of  square root of 1+(f'(x)) 2

Q: Determine the behavior of the functions defined below. Note that it is common to write f(x) → o" to ...

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Q: d. On what interval(s) of x is ƒ(x) decreasing? Preview e. On what interval(s) of x is f concave up?...

A: solution:-(d) f(x) is decreasing in the interval x∈-0.5, ∞(e)f(x) is concave up in the interval =DNE

Q: Solve each of the following equations for x by first writing the equation so that the left-hand side...

A: Follow next step

Q: Use the formula for the binomial series: m(m–1)---(m-k+1),★ + k! m(m-1) 2! m(m-1)--(m-k+1) „k if k=1...

A: expansion through maclaurin series .

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary functions....

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Q: Sketch the graph, indicate the focus, directrix, vertex, and axis of symmet Y^2 - 12x + 8y = -40 %3D

A: Topic:- geometry

Q: d²y if 2x2 + 5y² = 9. Find %3D dx2 Provide your answer below: -口 dy dx2

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: This is a problem of derivative and expansion of the series. Based on the formula of taylor series e...

Q: (d) Find the points(s) on the curve where there is a vertical tangent line. Find the exact point(s),...

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Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is in...

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Q: The cost of a can of Coca-Cola in 1960 was $0.10. The function that models the cost of a Coca-Cola b...

A: The cost function model, Ct=0.10e0.0576t represents the cost of the Coca-Cola by year. Where 't' rep...

Q: Find the radius of convergence and the interval of convergence. k + 7 k=0 Radius of convergence: Int...

A: This is a question of series calculation . Based on the general concept of the series we will find o...

Q: (x+Ax)³ – x³ lim Ax

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Q: Determine the larger volume. Assume there is a hemisphere which has a radius of 5cm was cut by a pla...

A: A sphere of radius 5. V = Volume of hemi-sphereV = ∫02π∫0π2∫05r2sinθdrdθdϕ r : radial distance from ...

Q: 1. If a stone is thrown vertically upward frosthe surface of the moon with a velocity of 10 meters p...

A: Follow the procedure given below.

Q: Question 2x² f(x) Let k(x) D 2x-2 Find k'(-1), given that f(-1) = -3, f'(-1) = -3. Provide your answ...

A: This question is related to derivatives.

Q: 7. Which of the following is a differential equation with homogeneous coefficient? (a) (y² – Vx² + y...

A: A differential equation of the formdydx=f(x, y)ϕ(x, y) is called a homogeneous equation if each term...

Q: Find the general solution of the given differential equation. x?y' + x(x + 2)y = e* y(x) = Give the ...

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Q: the following curves. 33. y= 2.x+ 3x² + 1 34. y = x -x - 6x 35. y= x³ - 3x? + 3x – 2 36. y = 100 + 3...

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Q: Find the Maclaurin series for the function. f(x) = x³ sin(x) F(x) = E n- 0

A: First I have written the Maclaurin series for sin(x),just use it and easily find the Maclaurin serie...

Q: Given Cost and Revenue functions C(g) = g° - 9g + 56g + 5000 and R(g) = - 3g + 2500g, what is the mi...

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Q: II. Solve the following systems of nonlinear equations: y +2x -3= 0 1. y + x2– 6 = 0 2. 4x2+ y² = 13...

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Q: we. ON 11. =? - ду (a) 3y – 3ry? (b) у — Злу? (c) 3y+3ry? (d) y+3ry?

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Q: 4. Which of the following represents the differential equation of the family of parabolas having the...

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Q: Determine the solution of the initial value problem 1. 5y" +y' = -6x, y(0) = 0, y'(0) = -10

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Q: 1. 2x +3 <7x- 23

A: topic- inequalities

Q: Water whose temperature is at 100°C is left to cool in a room where the temperature is 60° C. After ...

A: T=60+40ekt Substitute t=3 , T=90  90=60+40e3k90-60=40e3k3040=e3ke3k=343k=ln(34)k=-0.2883k=-0.096

Q: Convert the parametric equations of a curve into rectangular form. No sketch is necessary. x = Vt, y...

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