2) f(x) 3 F 2 8.x

Q: Solve the given differential equations: X 2. y' = , y(0) = -2 y+x²y

A: To solve the given differential equation.y'=xy+x2y, y0=-2

Q: If integration using u-substitution technique is used to solve for ∫2e2x1−e4x dx/square root of…

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Q: Find the derivative using logarithmic differentiation √x+1 y= (x+2) √x +3

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Q: Let S = { 1 − (−¹)ª | n € N}. Determine inf S and sup S. Justify. (-1)" n

A: Given : S=1--1nn|n∈N   To Find : inf S and sup S

Q: 4. Given vectors: ū=(4, 9), v = (-8, 15) and w=(2, 10) b) Write ū as a linear combination of and w.

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Q: Find the extrema of the following function on the given interval, if they are any, and determine the…

A: Follow the procedure given below.

Q: Solve the given differential equations: dy x-3 1. dx 2+y²

A: Differential equations

Q: Find the length of the arc of the curve from point P to point Q. 81 81 x-x² (-0, 32). Q(0,52) 2

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Q: 2x2+3x-2 26x2-x-1 lim x→ 3

A:

Q: he "Garbage Project" at the University of Arizona reports that the amount of paper discarded by…

A: We use a standard normal table to find the value  Given mean=9.4 standard deviation=4.2

Q: -1₁ - S. -3√ 42² + +81(1+z)² dy .dz y = Z =

A: The answer is given below:

Q: Evaluate [ (cos² 0 + 2 csc² 0 + sin² 0) do .

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Q: Circular Ring Method 3. R: y = x, y = 2x axis of revolution: x − axis

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 5) Find equations for the lines: h the noi e. The line through (1,1,1) parallel to the z-axis. f.…

A:

Q: In the process of calculating the inverse LaPlace of the function: F(s) = -29- arctan (²³3) you…

A: Given

Q: Consider a spring with constant k= 200 N/m, If the spring is compressed 4 cm, so the integral that…

A: work done in spring    W = ∫kxdx here  k = 200  upper limit in cm  2 and lower limit 4  so in meter…

Q: 3. Find the integrating factor e∫Pdx then find the general solution. 2(y - 4x2)dx + xdy = 0

A:

Q: Example: If w = f(x,y), find d²w dr² x = et, and y = 2t - 1

A: Here, w=f(x,y), x=et, y=2t-1

Q: d dx [3 sin³ (tan √x² + 3x²)] d [(x² + 1) cotx dx 3 cos x csc x

A: Given

Q: 2. Which of the following is correct in solving [2.xv 2x√√/2+x dx? (a) Substitution technique can be…

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Q: Evaluate exactly lim(1 + sinx)2cot: x→0

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Q: 5 Qu/ If w=f(u, v) = cos uv, u = xyz , v = 4(x²+y²) dw Prove that 0 at the this point…

A: Given problem:-

Q: Make a conjecture about the derivative by calculating the first few derivatives and observing the…

A: Given :d61dx61sinx

Q: Consider the following differential equation. (x + 1) + (x + 2)y = 4xe-x dx Find the coefficient…

A: Transient term in a general solution of a differential equation are those terms that tends to 0 as x…

Q: e. The line through (1,1,1) parallel to the z-axis.

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: x²-16 8. lim x-4x²+9x+20

A:

Q: 1) A pump is used to fill an inflatable mattress at a constant rate of 0.25 cubic feet per second.…

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Q: Let f and g continuous functions in R that satisfy at the same time all the following equalities :…

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Q: Verify that Rolle's Theorem can be applied to the function f(x) = x³ - 8x² +17x - 10 on the interval…

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Q: A 40-volt electromotive force is applied to an LR-series circuit in which the inductance is 0.1…

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Q: Name the quadrant in which the angle 0 lies sin 0>0, cos 0 >0 The angle 0 lies in which quadrant?

A:

Q: 3) Find equations for the lines: a 21 g. The line through (0.-7,0) perpendicular to the plane…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: The Great Molasses Flood At 1:00PM on January 15,1919, an unusually warm day, a 90-ft high, 90-ft…

A: We have to solve for force exerted by the molasses.

Q: /5 too dr Vx-1

A:

Q: 9. a. Explain why the Cartesian equation 2r-5y +3= = 2 does not describe the plane with normal…

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Q: 2. If ū=-27 +57-3k, then || is

A: We will find the value of u→ in the following step.

Q: R: y = x², x = 3, x-axis axis of revolution: x = 3

A:

Q: Reduce the rational expression to lowest terms. 2p² + 12p+16 2 4p²-4p-80 2p² +12p+16 4p²-4p-80

A: I am attaching image so that you understand each and every step.

Q: Find the exact length of the curve. y = 9 + ¹ cosh (8x), 0≤x≤7

A: The curve y=9+18cosh8x, 0≤x≤7

Q: 2. Use polar coordinates to evaluate √9-1² 2 L √4+x² + y² dy dx.

A: This is a problem related to integral of polar curves. Based on the substitution in cartesian…

Q: Find equations for the planes: d. The plane through P(2,4,5) perpendicular to the line x=5+t y=1+3t…

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

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Q: Which of the following gives the volume of the solid obtained by rotating the region R about the…

A: We know that the area of the curve y=f(x) , the X axis and the lines x=a ,x=b is revolving about the…

Q: Compute each of the following limits. (a) (i) lim 7x²5 x→-1 x²-25 (ii) lim X-5 x+5 (iii) lim x+2 x-2…

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Q: (x-2) dx = y + 2(x - 2)² dx

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

Q: The population of a town grows at a rate proportional to the population present at time t. The…

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Q: 1 50° || 5 1191 10% what is

A: Here we have to find the value a→·b→=?

Q: Use the method of variation of parameters to solve the differential equation d'y kdy - re dx2 dx and…

A:

Q: (a) ƒ (t) = €²t sin (3t)

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

Q: 1) In the triangle that determined by the points P.Q and R, find a unite vector perpendicular to…

A: