Evaluate the following limit: lim x ¹sin(8x). x → 0+ O O lim x-¹ sin(8x) = -8 vant lim x ¹sin(8x) = 1 vant lim x¹sin(8x) = 0 vint

Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 O A. B. ev eLny y O D.y O E.…

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Q: What is a suitable integrating factor that can be used to solve the equation dy x+2y - 4xy - e *…

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Q: Evaluate the integral π/ 10 S 3cos 5t sin 5t dt. 0

A: Please see the below picture for detailed solution.

Q: Solve for the value of C in the equation: O A. 1 OB. 2 O C.3 O D. 4 E. None of the Choices dy dx…

A: Find integrating factor of linear differential equation

Q: A baseball diamond is in the shape of a square with 50 ft sides. How far is it from home plate to…

A: A baseball diamond is in the shape of as quare with 50 ft sides. To determine how far is it from…

Q: 1. y' + ytanx = COSX; y(x) = (x + c)cosx; y(π) = 0

A: y'+ytanx=cosxy(π)=0proove that  solution isy(x)=(x+c)cosx

Q: What is a suitable integrating factor that can be used to solve the equation dy dx A. e B. 3 ex D.…

A: To find Integrating Factor.

Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 O A 4 OB.…

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Q: What is a suitable integrating factor that can be used to solve the equation dy cos(2x) = 0 O A. OB.…

A: To determine the suitable integrating factor that can be used to solve the equation.xdydx+2y-4xy-e-x…

Q: Shown below is the graph of the flow rate f(t) of a pipe, in gallons per minute. Here, t= the number…

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Q: X lim x0√1 + 8x - 1 ||

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Q: b) Find the area of the region described. The region inside the rose r = 2a cos 2β and outside the…

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Q: Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,…

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Q: Which of the equations below is a second order nonlinear differential equation? O A. B. 2 x²y - (1 -…

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

A: The given differential equation is dydx+ycotx=5ecosx, yπ2=1 This is a linear differential equation…

Q: The integrating factor (IF) of the equation y' - 2ycot2x = 1-2xcot2x - 2csc2x

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Q: lim x→7 x-7 14 x² - 7²

A: SOLUTION-

Q: indi the derivative  y=arctan² (x³)

A: Given,   y=arctan² (x³)    Find derivative of y

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: Sketch the region bounded by the curve x 2 = y and the line x = volume of the solid generated by…

A: solution:-the region bounded by y=x2-2 & x=y+2revolving around y=1

Q: Evaluate the derivative of the following function. 1) 6x H(x)= (5x +

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Q: Use the first derivative test to determine all local minimum and m points of the function y=x³-6x²…

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Q: A contour map for a function f is shown. Estimate the value of fy(3, 16) 25- 20 15- 10 5 60 fy(3,…

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Q: 8. Find the limit of f(x) = lim f(x)= 4- 818 (Type a simplified fraction.) lim f(x) = 8118 (Type a…

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Q: g(x) = 3x + 6 x 10

A: We need to evaluate the limit.

Q: K A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges…

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Q: Find the length of the curve. 1 10x³' y = 6 + X 2≤x≤4

A: y=x56+110x3,  2≤x≤4

Q: Evaluate using integration by parts or substitution. Check by differentiating. (2x²-7x) e7x dx √(2x²…

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Q: Which of the following equations is NOT an exact equation? | OA. (2x sin y + y)dx + (x² cos y + x)dy…

A: Exact differential equation A first order differential equation M(x,y)dx+N(x,y)dy=0 is called an…

Q: 1. Given the vectors a³ = (2, −1, 3), b` = PQ` where P(1, 1, 1) and Q(5, 1, −1) and c³ = i̇ + j³ +…

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Q: Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an…

A: Given query is to apply sine law and complete the triangle.

Q: Find y'(x). y'(x) = y = √-1 + 2x At what point on the given curve is the tangent line perpendicular…

A: Given query is to find the derivative and the point where slope of tangent is perpendicular to the…

Q: Given the differential equation: (4xy + 3y² - x) dx + x(x + 2y)dy = 0 The solution to the…

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Q: The graph of f(x) below has a hole when x=_ and y=

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Q: Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y + 3x) dy dx…

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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: Which of the following is a non-homogeneous function? tan³y/x xLnx − xLny - xy + y² (y² + v²)3/2 43…

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Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: Here we can create the required polynomial function in the below steps.

Q: Question 20 Obtain the differential equation whose general solution is y = C₁ + c₂e³x A. B. D. E. y"…

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Q: Find the exact length of the curve. X = t 2 + t y = In (2 + t), 0≤t≤1

A: Given: x=t2+t, y=ln(2+t) We know that exact length of the curve is given by  s=∫t1t2dxdt2+dydt2dt

Q: Exercises  tell how many units and in what directions the graphsof the given equations are to be…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: A central angle in a circle of radius 8 is subtended by an arc oflength 10pai. Find the angle’s…

A: Given: Length of arc, l=10π units Radius , r=8 units To find the central angle’s radian and degree…

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: If f(x) f'(x) = f'(1) = 2 sin x 3 + cos x 2(1+3 cos(x)) (3 + cos(x))² then

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

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

Q: Can someone compute this into decimal form. f'(4)=-sin(4)-3sec²(4) Thank you

A: we already have f'(x)=-sinx-3sec²x so,f'(4) =-sin(4) -3sec2(4)

Q: Find the limit of each of the following sequences, using L'Hopital's rule when appropriate. √n Vn+1

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Q: The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy + 2y)dx + (2y³ + 2x²y + 2x)dy…

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Q: Which of the following equations is NOT an exact equation?

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Q: Where Given the vectors 2 = ( 2,-1, 3), B = PQ P (1, 1, 1) and Q (5,1, -1) and C = T J + 3R . • Find…

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