Evaluate the following integral. r/4 1 (s secx- cos cos sx)²dx 0 x/4 ļ (secx- cos x)²dx= 5 3 4 8 0 (Type an exact answer. Use parentheses to clearly denote the argument of each function.)

Q: Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x) and…

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Q: A population of 470 bacteria is introduced into a culture and grows in number according to the…

A: Given problem:- A population of 470 bacteria is introduced into a culture and grows in number…

Q: Which of the following functions describes the graph of h(x)? h(z) -10 h(x)= Oh(x)= 3x +2 x-1 3x +2…

A: Given query is to find the function from the graph.

Q: Find the solution of the given initial value problem. y’’+2y’+2y=0,     y(π/4)=2, y’(π/4)=-2…

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Q: 1. Evaluate the lim [In (x)] using table of values. Table A (for x values that approaches 1 from the…

A: SOLUTION-

Q: Find the general solution of the given differential equation. y’’+2y’-8y=0 topic: complex roots of…

A: Explanation of the answer is as follows

Q: Q5: Use the method of variation of parameters to find the general solution to the following…

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Q: The plane x + y + 2z = 12 intersects the paraboloid z = x² + y2 in an ellipse. Find the points on…

A: Suppose the point nearest to origin with the condition that it is not the ellipse that is obtained…

Q: Consider a function f that is continuous on [-2, 4] with f'(x) = 0 whenever x = 3 or x = 5. Suppose…

A: Explanation of the answer is as follows

Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

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Q: R: x² + 3y = 4 and x – 2y = 4.

A: The region is bounded by the curve x2+3y=4 and x-2y=4

Q: x+2 lim x-2x²+4x+4

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Q: Consider the following curve. f(x) = (x-2)/(x^2) a. Determine the domain of the curve. (Enter your…

A: given f(x)=(x-2)x2a.Determine the domain of the curve.b.find y'and y''

Q: d dx [x² tan x]

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Q: Answer 4,5,6

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Q: *************** ********* Identify the open intervals on which the function is increasing or…

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Q: 1 If f(x) = 8 tan¯¹(8 sin(2x)), f'(x) =

A: Differentiate

Q: Find the value of an investment of $25,000 for 13 years at an annual interest rate of 3.15%…

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Q: Show that the solution y(t) of the initial value problem has the Laplace Transform y" + 2y' - 3y = 6…

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Q: Consider the following figure. B A A D Given: AABC, whose sides are 25 in., 17 in., and 26 in. Find…

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Q: Find the eneral integration of th following differential equation xy-Y Xtan y x

A: Concept: Homogeneous differential equation: By integrating the provided differential equation, the…

Q: a = [0,-1,7] and b = [2,4,-3].

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Q: Solve the given initial-value problem. dx y X= = 4y2, x(6) 1 dy Give the largest interval I over…

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Q: 5) An equation of the of the plane passing through the points P(0,2,1), Q(2,1,2), and R(3,3,1).

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Q: given by v(t) = 7e", where t stands for time. (Note: Find the integral of the function (t).) 2.…

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Q: Which of the following graphs represents the function g(x) = x²(x + 1)(x − 2)? 2 4 2 * 0 4 0 O 4 2 P…

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Q: Find the area of the surface generated by revolving the curve y = 2√x, 1 ≤ x ≤ 2, about the x-axis.…

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Q: b. |ā + (bx c)|

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Q: Find the determonant of the matrix A = 1 -1 -2 2 1 -21 -1 4 2 2 1 3 -2 1 2 -31

A: Topic = Determinant

Q: d [x2 + dx|x4 d dx [(x2 + 1)50]

A: To evaluate the following.1 ddxx2+1x4-12 ddxx2+150

Q: (2x-2) dx sinx dx 2. 3. √xdx 4. J² (²2x²+4x-2) dx 5. So (cosx+tanx)dx 1/1/4 6. Jo ¹/2_dx =dx √1-x²

A: Solve by integration

Q: +7+ 3xf x for x ≥ 1, where x is the number of rackets produced per hour. For a company that…

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Q: State the order of the given ordinary differential equation. (1-x)y" - 4xy' + 6y = cos x Determine…

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Q: Page < 4. The brightness of stars is expressed in terms of magnitudes on a numerical scale that…

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Q: The range R and the maximum height H of a projectile fired at an inclination 0 to the horizontal…

A: Note: Since, in the image of the question posted by the student, it is not clear how many place to…

Q: (b) In an oil refinery, a storage tank as shown in Figure 1 contains 2000 gal of gasoline that…

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Q: b) Give the augmented matrix associated to the system of linear equations above. Answer: sin (a) ə…

A: The simple matrix

Q: 2x2+3x-2 26x2-x-1 lim x→ 3

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Q: Suppose you start with one liter of vinegar and repeatedly remove 0.13 L, replace with water, mix,…

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: 1. lim(2x² + 2x - 3) X-4 3.9 X f(x) 3.99 99 3.999 4 ? 4.001 4.01 4.1

A: To find: limx→42x2+2x-3

Q: Find the second derivative of the function. f(x) = 5(2 − 7x)ª

A: Given query is to find the second derivative.

Q: 5. ²+²=2xy 6. 2x + 2y + 2y' + 1 = 0 dy dy 7.

A: Solution is here

Q: Problem 7. The base of a 50-foot ladder is being pulled away from a wall at a rate of 10 feet per…

A: The base of a 50-foot ladder is being pulled from a wall at a rate of 10 feet per second. To…

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) -1 lim (-6 +h)-¹ + 6-1…

A: L'Hospital rule:- If limx→0f(x)g(x) is of the form 00 then limx→0f(x)g(x)=limx→0f'(x)g'(x)Continue…

Q: A. Solve the following Initial Value Problem (IVP): y + 3y + 2y = 6e at y(0)=1 and y (0)=2

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: Solve the initial value problem y"+y=f(t), y(0)=y'(0) = 0, (21 2t if 0 1

A: Here is the solution of the given problem. We solve this problem by using Laplace transformation

Q: A can is dripping out water at a rate of r(t) = 12/17 If the can held 50 cm³ of water at time t = 1,…

A: If rt is the rate of dripping out water from a can then volue of water dripping out after t time is…

Q: State

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Q: Find the angle between the vectors and .

A: Given vectors a=-2i-j+3k b=2i+j-3k

Q: Find an explicit solution of the given initial-value problem. √1-y² dx - √1-x² dy = 0, y(0) = 113 2…

A: Here in this question, we have to find out the solution to the given differential equation.