Determine whether the improper integral converges and, if so, evaluate it.   ∞ 0 5x dx (3 + x2)2

Q: nd the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer…

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Q: 1 The region bounded by the graph of f(x) 1 + x² the x-axis between x = 0 and x = 6 is revolved…

A: Here we have to find the volume about given x-axis.

Q: Compute the Fourier series for z+z on (-=,=).

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Q: 3. Let y = (f(x) + 5x²)4 and suppose that f(-1) = -4 and = 3 when x = -1. Find f'(-1). dx

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Q: 12-14 Simplify the expression. 12. tan(sin ¹x) 13. sin(tan ¹x) 14. sin(2 arccos x)

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Q: you

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Q: Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for…

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Q: Then (fofof)(x) = || (gogog)(x) = ((fog) - (gof))(x) = ((f+g) o (f-g))(x) = f(x)=2x-1 and g(x) = 3x…

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Q: Sketch the graph that possesses the characteristics listed. fis concave down at (1,4), concave up at…

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Q: A rectangular piece of land has dimensions 1050 ft by 550 ft. Find the area of the land to be…

A: The length of the rectangular land, l = 1050 ft Width of the land, w = 550 ft To evaluate: The area…

Q: Let F(x, y) = 1 + √√1 − y². 1. Evaluate F(3, 1). Answer: F(3, 1) = 1 2. What is the range of F(x,…

A: Let's solve for function value at given point and its range.

Q: Find the particular solution of the following equation by first finding its general solution: y''…

A: Given, y'' - 4y = 10

Q: Determine if the improper integral converges or diverges. 6- sin p 62 converges Odiverges do

A: We need to choose correct option.

Q: Find a general solution to the differential equation: dx/dt = = x + e^t -- please show all work in…

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Q: Let A = {7, 2, 6, 8, 3, 5} B = {4, 2, 8, 9} and U be the universal set of natural numbers less than…

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Q: Find the velocity, acceleration, and speed of a particle with the given position function. r(t) =…

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Q: sy(

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Q: G(x)= x³ +3x+2 x+2 [[x]] + 1 -1-x-21 - 4 x+3 + 1 x-r if x<-1 if -1 ≤ x 1 if xz1

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Q: Given f(x, y, z) = x²y³z - 3xy²z³ + 5x²z - y³z, find fxyz

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Q: Evaluate dv = dx). [tan=¹(a)dr. (Hint. Use integration by parts let u = tan ¹(x) and

A: We have to evaluate the integral.

Q: (a) How long will it take an investment to double in value if the interest rate is 4% compounded…

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Q: Let u, ER" prove that |uv|≤|||||||||

A: This question can be solved using the following conceptsa. Dot product of two vectorsb. Modulus of a…

Q: 1. Graph the following function on the board: f(x)= 0 1+x 1-x 0 -∞0 < x < -1 -1<x<0 0≤x<+1 +1<x<+∞o

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Q: Find the absolute maximum and minimum values of each function over the indicated interval, and…

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Q: Question 1 dy 1) Consider the equation 25x² +9y² = 225. Use Implicit Differentiation to find da (c)…

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Q: Find the derivative of the function using the definition of derivative. F'(v) = F(v) = V V + 3 3…

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Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: We can find the limit .

Q: 2. Circle the function if it is exponential, or if it is a transformation of an exponential…

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Q: answer the following questions about curves defined by parametric equations. Make sure to include…

A: solution is given below..

Q: Find the general solution of each of the following. J.. 1 1. in 2. y tan² x dx + In¹y dy = 0 000² v…

A: Please see the below picture for detailed solution.

Q: y ( x ) = (₁ e ² + ( ₂ e 2X + - 3e³x; y(0) = 0, y'(0) = 0

A: Given:- yx=c1ex+c2e2x+3e3x y0=0,y'0=0

Q: Find dy dx 14.) y = x¹ - 7x

A: To find derivative

Q: Solve for the complete solution of the differential equa y" − 6y' + 9y = 0; y(0) = − 1, y'(0) = 2.…

A: Topic:- differential equations

Q: Solve the integrals: (1) (c I₁ = 1 |x| x² + x| dx

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Q: (1.1) Calculate the Laplace transform of the following function from first principles: f(t) = = 3t -…

A: Laplace transform of a function f(t)  using first principles is Fs=Lft=∫0∞e-stf(t)dt

Q: 51-52 Find an equation of the tangent line to the curve at the given point. 51. y = e* cos x + sin…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Find zxand zyif z = x² tan-¹-y² tan-¹

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Q: (b) dy 3-4012 4xy + by2 ; dz = (1) y(1) = -1

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Q: Find dy dt || dy dt for y = sin 2 (3nt – 4).

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Q: Calculate the value of the derivative of the function:  y = cos (sin x) at the point x = 3π/2 to 2…

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Q: 1. Three vectors in space are given as = 3x + 2y + 42 K L = 2x − 3y + 2 - M = -x-4ŷ in cartesian…

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Q: Complete the table and predict the limit, if it exists. (Round your answers to three decimal places.…

A: Let's find limit is exit or not.

Q: Use the Chain Rule to find dz/dt. z = xy² - x²y, x=t² + 1, y = t²2² - 1

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Q: Differentiate the function. y = (5x-4) (3-x3) 3 dy dx

A: Given :                    y=(5x-4)³(3-x³)³ Here, it is in the form of product of two functions.…

Q: 4. rdp-(p+√pr) dr=0

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Q: 9) A rectangle has one corner on the graph of the line y = -x² + 6, another at the origin, a third…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: then m = (q²b²³) 1/10 9-1/261/5 = and n = qmbn 1/10

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Q: Show that xzxx+yzxy = y²Zyy if z = xy + yln(xy)

A: To prove the given result find zxx,zyy,zxy and substitute in the given equation.

Q: (a) Show that y = e(c₁ cosa + c₂ sin x) is a general solution of y" + 2y' + 2y = 0. (b) Deter- mine…

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Q: and- I need a clear answer by hand, not by keyboard | dybala Determine the general solution for the…

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