Let R be the region bounded by the follow ing curves. Find the volume of the solid generated when R is revolved about the given axis. y = Ix1 and y = 2 - x²; about the x-axis

Q: Show by induction that if (n) is a positive integer, then ((n^3) - n) is divisible by 6.

A: Given statement is

Q: The total annual spending by tourists in a resort city is $200 million. Approximately 60% of that re...

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Q: find the curl of each vector field F. F = (xy + z)i + (yz + x)j + (xz + y)k

A: Consider the equation: The delta operator is given by :

Q: First-order linear equations Find the general solution of the following equation. y '(x) = 2y + 6

A: We first separate the variables  

Q: Trigonometric integrals Evaluate the following integrals. ∫sin2 3x dx

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Q: Please solve the below given equation

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Q: Use an identity to solve the equation sin (x + π/4) + sin (x - π/4) = 1 on the interval [0, 2π).

A: We will use sin(A+B)=sinAcosB+cosAsinB and sin(A-B)=sinAcosB-cosAsinB    

Q: (1– 1)y' – y² +x²y+2x = 0, Y1 = -x² %3D

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Q: lim x→π/16    tan(48⋅x) =

A: Given limit:

Q: Describe how the name hyperbolic function arose

A: Consider the equation of the semicircle is, Consider the equation of the hyperbola is,

Q: Find the volumes of the regions. The tetrahedron in the first octant bounded by the coordinate plane...

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Q: In each of Problems 5 through 11, find the general solution of the given differential equation. 5.y″...

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Q: Use the Intermediate Value Theorem and a graphing utility to approximate the zero of the function in...

A: We find f(x) at x=0 and x=1 Since, f(0)<0 and f(1)>0 , so by intermediate value theorem there...

Q: What are the eigenvalues and vectors of this matrix? [1,2 ,3 4,5,6 7,8,9]

A: Given data:     The given matrix is: .   The expression for the characteristic equation is, Substit...

Q: Suppose that f is differentiable function at x= 3and f (3) = 0, f (3) =1. Then lim f(h+1)- f(7-h*) (...

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Q: The first term is 3500, and the common difference is 15. Which term of the sequence is 2795?

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Q: Simplify the expression, should equal 1! Just show me the steps

A: Given: cos(x) cos(-x) - sin(x) sin(-x)

Q: Describe the interval(s) on which the function is continuous. f(x) = sec x/4

A: The denominator can not be 0.  

Q: Determine an equation for the tangent line to f-(x) at (4, 7) given that y-4= (x - 7) is an equation...

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Q: Estimating errors. Use the remainder to find a bound on the error in approximating the following qua...

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Q: Is the following function a valid probability density function? 3x² – if - 1<x< 1, f(x) = otherwise....

A: 1. f(x) ≥  0 for all x

Q: Begin by graphing f(x) = 2x. Then use transformations of this graph to graph the given function g(x)...

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Q: Write the equation ln A = 3 in exponential form.

A: We will use the exponential form of the natural logarithm.  

Q: Refer to image

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Q: Approximate the number 6-1.2 using a calculator. Round your answer to three decimal places.

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Q: Use the specified substitution to find or evaluate the integral.

A:   We need to use the specified substitution to find or evaluate the integral.  

Q: Evaluate the integrals in ∫er/1 + er dr

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Q: Derivatives with general logarithms Compute the derivative of the following function

A: We use the change of base property of log. Then we use the chain rule of the derivative. 

Q: I am really confused about the sandwich theorem. I did not understand the lesson and would love to u...

A: Given data:     The sandwich theorem states that if f(x), g(x), and h(x) are the three functions whi...

Q: A random variable Y has probability density function g, given by for 0 < y < 1 8(v) = { 2y g(y) = ot...

A: For the given random variable Y, its pdf is

Q: Use the graph to find the limit (if it exists). If the limit does not exist, explain why.

A: From the graph we see that, when x is close to 3, then y is close to 1.  So the limit exists.   

Q: Spirals Graph the following spiral. Indicate the direction in which the spiral is generated as θ inc...

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Q: Find the limit limx→π/2(sinx)tanx.

A: We use tan(x)=sin(x)/cos(x)

Q: Find all the antiderivatives of the following function. Check your work by taking derivatives. ƒ(x) ...

A: We find the antiderivative of f(x). C=integrating constant  

Q: Give an example of each of the following: (a) A natural number (b) An integer that is not a natural ...

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Q: Solve compound inequality. -6≤1/2x - 4 &lt; -3

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Q: The mad Dr. Frankenstein has gathered enough bits and pieces (so to speak) for 2-1 + 2-2 of his crea...

A: Dr. Frankenstein has gathered bits and pieces is,

Q: Determine the derivative of the function y=xlnx−x.

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Q: Give the slope and y-intercept of the line whose equation is y = (2/5)x - 1. Then graph the line.

A: We will compare the line with y=mx+b Comparing we get: m=slope=2/5 and b=y-intercept=-1  

Q: find an appropriate graphing software viewing windowfor the given function and use it to display tha...

A: We will use a graphing calculator to graph the function  First I am taking [-5,5]x[-5,5] viewing wi...

Q: If f(x) = x' + 1, then (a) the value of f at x = -1 is f(-) = (b) the value of f at x = 2 is f() = (...

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Q: Find equations of the tangent line and normal line to the curve  y= x sqrt x  at the point  (1,1) . ...

A: Given curve: Let the slope of the tangent line to the given curve is m. And the slope of the normal...

Q: evaluate the given integral.

A: Then we use substitution  

Q: Graph each side of the equation, sin x - sin x cos2 x = sin3 x in the same viewing rectangle. If the...

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