Evaluate the following integral. 4x Jetz 4* sin(2x) dx =

Q: dy What is the IF for solving the linear equation: x dx O O O O A. 3 X2 B. 3x 2 C. 3 -Lnx D. E. 3x e…

A: It is linear differential equation

Q: dy 3y What is the IF for solving the linear equation: x + = dx COSX,x>0

A: The given differential equation, xdydx+3y2=cosx, x>0 We have to find the integrating factor

Q: f(x)= (ln x)^3 f'(x)=

A: Given, f(x)= (ln x)^3

Q: 5. Logarithmic Differentiation Method (a) Let y = n. Compute dy by using logarithmic…

A: solutions:-(a) y=xlnxtaken log both sideslny=lnxlnxlny=lnxlnx=lnx2differentiate both sides w.r.t…

Q: Determine the degree, order, and whether it is linear or non-linear 3 (y") ³-4y²= 10e 5x First Order…

A: Topic- Differential equations We are given an equation, (y'')3-4y2=10e5xOrder=Order of the…

Q: 13. Suppose that lim f(x) = 13 and lim g(x) = -7. Find the following limits. X-4 X-4 a. lim…

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Q: What is the standard form of this linear equation in one variable: (y + 1)dx + (4x − y)dy = 0? |…

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Q: Determine the order and degree of the differential equation, 3x dy4 +5x² 3 (d²y) dx² - xy = 0.

A: Determine the Order and Degree of the differential equation.

Q: Solve for the value of C in the equation: (2xy4e³ + 2xy³ + y)dx + (x²yªe¥ − x²y² – 3x)dy = 0 when…

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Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

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Q: A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the…

A: Given :- dNdt=-0.069N

Q: Determine the order and degree of the differential equation, 3x- + 5x² (d²y) ³ - 3 A. First order,…

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Q: Graph the function y = sqrt(|x|)

A: Given data:- The given function y= sqrt(|x|)

Q: In this problem you will calculate the area between f(x) = x² and the x-axis over the interval [3,…

A: a) ∆x=b-an

Q: Write an equation for each line. 15. through (2, 2), y-intercept 10

A: since you have posted multiple questions i can do first question as per our company guidellines.…

Q: 2. 8[][

A: The objective of the question is checking the convergence or divergence of the given series.

Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/² when x = -1 and y =…

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Q: Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1 - A. 1/4 B. 1/2 C. 3/4…

A: Find integration factor first as it is linear differential equation

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Q: Determine the solution of the differential equation: dx dy y 4² + X y

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Q: Consider the function f(x)=eXx. Select all that apply. Select 3 correct answer(s) f(0) is positive.…

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Q: Find the total area bounded by the graphs of f(x) = 3x³x² - 10x and g(x) = -x²+2x. O 32 units² O 8…

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Q: If you roll a 1-m-diameter wheel forward 30 cm over levelground, through what angle will the wheel…

A: Given data:- The given you roll a 1-m-diameter wheel forward 30 cm over level ground. Formula used,…

Q: Graph each of the functions in the same viewing rectangle. Describe how the graphs illustrate the…

A: Concept used: Graphing A graph of a function is a line that represents the function on a coordinate…

Q: Problems: 1.(x³ + xy² − y)dx + (y³ + x²y + x)dy = 0 2. (ex siny + ey)dx - (xe-y-e* cosy)dy = 0

A:

Q: 17. Find the limit. x+5 lim 2 X-5x + 6x + 5 x+5 lim 2 x-5x + 6x +5 (Type an integer or a simplified…

A: Factorise the denominator x2+6x+5 and cancell the common factor of numerator and denominator.

Q: Let p, q and r be the propositions: p: Wild foxes have been seen in the area. q: Hiking is safe on…

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Q: Given the differential equation: 2 y' + ²y = 6x²

A: To choose the appropriate method to be used to solve the given DE. Method 5: Exact Equation Method…

Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/2 when x = -1 and y =…

A: We have to find the value of c.

Q: Devise an exponential decay function that fits the given data, then answer the accompanying…

A: Here, the equation used is: P=P0ekt...(1) where P is the pressure of the atmosphere at t=0 and k is…

Q: hich of the following equations can be made into a linear differential equation? DA. (x² + xy)dy -…

A:

Q: For # 1-12, differentiate 1₁ f(x) = (x² - 3x + 5)35 3 2. g(x) = √²-5 3/x2-5 3. y = sin x² 4. y =…

A: We need to differentiate function.

Q: A mathematical model for the average of a group of people learning to type is given by N(1) (2 hours…

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Q: Question 2 Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1 A. 1/4 B.…

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Q: Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0 and the plane 3x +2y + z = 6.

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Q: Graphing the Cube Root Function(a) Determine whether f1x2 = 23 x is even, odd, or neither. State…

A: Given function is cube root function i.e., f(x)=x3

Q: For the piecewise linear function f(x) graphed below, find the following. (If an answer does not…

A: Given: To find: limx→2- fx , limx→2+ fx, limx→2 fx

Q: Solve for the value of C in the equation: (2xy¹ey + 2xy³ + y)dx + (x²y4eY - x²y² - 3x)dy = 0 when…

A: uation Given differential equation of the formMdx+ Ndy=0

Q: 4. Linear Equations b. 2y(y² - x)dy = dx

A: We can solve this as follows:

Q: Rewrite the following expression in terms of exponentials and simplify the result. (cosh 3x - sinh…

A: We need to rewrite the given expression in terms of exponentials.

Q: A (B) f(x) is continuous at.x=3 D lim f (x) exists x-3 (C) f(3) exists Based on the graph above,…

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Q: Find the exact length of the curve. x = 5 + 12t², y = 6 + 8t³, 0≤ t ≤ 3 12117-1)

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Q: 1 † (OM - ON) - M . If OA es OB. U O D. e-5 ys ly = then what is the integrating factor?

A: Key points: Consider the differential equation M dx + N dy = 0. If this equation is not exact, then…

Q: 1. Separation of variables/ a. xy³ dx + (y + 1)e *dy = 0

A:

Q: dy Solve for the value of C in the equation: + ycotx dx O A.-5 OB. 5 OC.-4 O D.4 O E. None of the…

A: It is linear differential equation.so we find integrating factor

Q: 5) Square PQRS with side length x is subdivided into four triangular regions as shown such that area…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Which of the following is a non-homogeneous function? O O tan³y/x | xLnx − xlny x³ - xy + y² (y² +…

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Q: Solve for the value of C in the equation: dy - (y + xy5) dx = 0 when y(0) = 1 O A. 1/4 O B. 1/2 O C.…

A: First we will integrate the given differential equation and then find the value of C at given…

Q: 23. The accompanying figure shows the graph of y = -x² shifted to two new positions. Write equations…

A: Given: The figure shows the graph of y=-x2 shifted to two new positions. To write the equations of…

Q: ntegrate the following. I 8x 12e dx - =

A: Given query is to find the integral.