1 So 2t en + e-2t ezt - e-at dt

Q: Use the linear approximation to estimate In (√0.99).

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Q: Find the Integrating Factor (I.F) of the following linear differential equation: (1 + ²) + y =…

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Q: Test for exactness, then solve.  ey dx + (2y + xey) dy = 0

A: This question is related to differential equations, we will solve it using given information.

Q: c4 So So (6x² +9y²) dx dy

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Q: Solve the following matrix equation for a, b, c, and d. a-b b + c |-|8 8 3 88 3d+c 2a - 4d a = b =…

A: We will find the value of a ,b ,c ,d by solving the given matrix equation in the following step.

Q: Find the surface area generated b rotating the portion of the parabolic arc x = y^2 from x = 0 and x…

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Q: Please graph the function of D(t)= 28sin(360/365 t - 1.4)

A: Let's graph the given function.

Q: Why is it =10πr33? particularly, why is the value 33?

A: Let's solve.

Q: Find the equation of the family of curves having the given slope, and the equation of the curve of…

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Q: Suppose that the number of crates of an agricultural product is given by 11xy-0.0002x² - 5y Z= 0.03x…

A: Suppose that the number of crates of an agricultural product is given by z=11xy-0.0002x2-5y0.03x+4y…

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: The equation of the curves are: C1: y = x2 ⇒ x = y                 for first quadrantC2: x = y2 To…

Q: It is projected that the population of a certain town will be P(t) = 2t+4+³/2 + 5000 where P(t) is…

A: Rate of increase of population=P(9)-P(0)9-0

Q: - 4. Find the area bounded by y = x - x² and y = x(x − 2)(x+2).

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Q: What is the y-coordinate of the centroid of the plane region bounded by y = x^3 and y=x^2? O 2/5 3/5…

A: We can solve this as follows:

Q: What is the integral of (2 sec^2x - sinx) dx? * O 2 cosx+tanx + C 2 tanx + sinx + C 2 tanx + cosx+C…

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Q: 1. -3 Given that 9+x² following functions: (−1)n+1 Σn=0 32n+1 1. f(x) = 5 arctan x2n. Obtain the…

A: We have to obtain power series representation.

Q: Let f(x) = e2sinz 1. Use the local linear approximation of f at x = 0 to approximate e2 sin(0.01

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Q: Evaluate the integral of 3dx/(2x^2 + 4) from 0 to 0.2 *

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Q: II. Evaluate the following integrals. 3. ²|2 - 2º| da

A: Given: ∫03|2-2x|dx

Q: Solve the non-homogeneous linear recurrence relation. (note: the non-homogeneous part is a constant…

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Q: Use the Second Derivative Test to find all relative extrema. (a) h (x) = x - 2 cos x, [0, 4π]

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Q: Find the equation of the line tangent to y = e The equation of the line tangent is y= at x = 1 - In…

A: Given query is to find the equation of the tangent.

Q: Determine the values of r for which the differential equation y" +9y' + 20y = 0 has solutions of the…

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Q: 3. Water is flowing into a vertical cylindrical tank at the rate of 24 cubic ft. /min. if the radius…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Determine whether the series k=1 3\k-1 converges and if so, find its sum.

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Q: Answer

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Q: 8 9 - 4e²™ dx Please approach doing this integral by hand with the following steps: First, make a…

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Q: 10x-3y For the function f(x,y,z)= 8z + 1 fx=0 find fx. fy. fz, and fyz-

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Q: VI. Determine the instantaneous rate of change of the functio: sin (³) f(x) = V² siz r³ 1 + √t at x…

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Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

A: We sketch the given region using a graphing calculator as shown below:   The shaded region is…

Q: y-coordinate of the centroid of the plane region bounde 22 What is the y = 2x + 1, x + y = 7, and x…

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Q: Perform the integration. x-1 S= dx x² + 5x + 8

A: ∫1x2+a2 dx =1atan-1xa+C

Q: As part of a chemical experiment, a scientist determines that the number sodium in a chemical…

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Q: 1 - cosh x lim x→0+ ln(x² + 1)

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Q: Approximate the area beneath y = sin x on the interval [o, π] using the Trapezoidal Rule with n = 4…

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Q: III. Directions: Find the derivative of the given functions with respect to x using the limit…

A: i) f(x)=3x2+5x-7ii) fx=12x2-9x

Q: 3. Find f'(a) if f(x)= e7x 2x + sin³ x

A: In this question, we want to differentiate the given function f(x) with respect to x.

Q: 1. Why is it important to use the six trigonometric ratios in getting a missing angle value?

A: The six trigonometric ratios are sine, cosine, tangent, cotangent, secant, and cosecant. Basically,…

Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

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Q: Evaluate the limit using the L'Hopital's Rule. 1 - cosh x lim x→0+ ln(x² + 1)

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Q: f(x) = 4√√x + 2x¹/2 - 8x-7/8 +x². f(x) +2 1 x3 = ²325/2 - 2x³/2+1/32²³- x³ - 2x² + x −1. 9

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Q: 5. Find the area bounded by y = sin √x and y = 0 on the interval [0, π²].

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Q: A ship leaves port travelling North West at 12 knots. A second ship leaves the same port 3 hours…

A: Given: Let first ship be Ship A and second ship be Ship B. Speed of ship A = 12 knots =12 nautical…

Q: y s 5 4 -2 -2 The diagram shows the shaded region bounded by the curves y = x² + 2, y = 4 - x, y = x…

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Q: a. A cylindrical container that is open at the top is to be made from two kinds of material. The…

A: note : as per our company guidelines , we support one question in one request (because these two…

Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

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Q: (x² - 12x + 9) dx (x²-3x + 2)² 2. √(x²

A: Given: I=∫x2-12x+9x2-3x+22dx   As we know that; The Power Rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: 4. If a 32 foot chain is hanging (balanced) on a metal peg on a wall. At time t=0, with the chain…

A: Given that,

Q: 3x² - 6x² + x (36²-6x² x)]d² X

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Q: 2. Find the interval of convergence of the power series & 3x गय

A: