Let f(z) be a continuous decreasing function defined for z > 0. Let S(x) = f(t) dt %3D and S(1) = 1. For any a > 0, the area bounded by the following is 3S(a): (a) the line joining the origin and the point (a, f(a))

Q: Let f (x) = 6 sinh 1(tan(x) , O < x < 5. Find the slope of the line tangent to the graph of f at the…

A: Given: Here, we need to find the tangent line to the graph of f at the point on its graph where…

Q: Is f(x)= Vx + 1 continuous at x == -1

A: Draw the graph and check continuty with help of limit of function.

Q: Identify a function f that has the given characteristics. f(-5) = f(1) = 0; f '(-2) = 0, f '(x) 0…

A:

Q: 3. Let X be the amount of an insurance claim which has following pdf: Kx? (4 -x), 0 <x < 2 (x) %3D…

A: f(x)=Kx2(4-x) ,      0&lt;x&lt;20,            otherwise

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: 3. Let X be the amount of an insurance claim which has following pdf: Kx (2-x), 0<x <3 f(x) = 0,…

A: Given : The pdf of random variable x is : f(x)=Kx2(2-x),0,x&lt;30,elsewhere We want to find value of…

Q: The sale of a certain product has marginal revenue function given by R'(p) = 300-25p , where p is…

A: Given data: The revenue function is given by, R'p=300-25p Increase in price is $8.00 to $10.00.…

Q: The graph of ƒ is shown. Let A(x) be two area functionsfor ƒ. Evaluate F(8)

A: &amp; Fx=∫4xft dt

Q: Identify the plot below that represents a function f(x) that satisfies the following conditions:…

A:

Q: 3. Let X be the amount of an insurance claim which has following pdf: Kx2(2-x), 0<x <3 0 <x f(x) =-…

A: It is given that, x be the amount of claim with pdf fx = Kx2 2-x,0&lt;x&lt;30,elsewhere

Q: Show that the function f(x) = 1/2 e−|x|IR(x) is a valid pdf.

A: Let the function is given by, fx=12e-x      for Rx Further we simlified it as, fx=12ex      for…

Q: Please

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Q: Let f(x) = 1- 5x2. Use the limit definition of the derivative to show tl f'(x) = –10x

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Q: Find the x value(s) for any relative extrema. Use the Second Derivative Test to determine if this is…

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Q: Determine if the sequence {a,} converges or diverges. Find the limit if the sequence converges. n 6n…

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Q: fhow thot te function f depined by f(XrY) = 1 (x,Y) =(1,-リ - 1) %3D x2 +y (x, y) F (I,-1) * t y is…

A: We use the sequential definition of continuity to solve this problem.

Q: DO NOT include spaces in between characters. * Given F(x)= f(x)g(x) and f(2) = -3, f'(2) = 4, g(2) =…

A:

Q: Consider a function f continuous and differentiable on R with f(2. 5) = -3. 1 and f'(2. 5)=-0. 2.…

A: We have to find

Q: Let g(x) = | F(t) dt, where fis the function whose graph is shown. y f 12 1 (a) Evaluate g(x) for x…

A: Given The given integral is  and the given graph is  Apply formula  The area of the right angle…

Q: Use a local linear approximation to estimate the following y-values 1. f(3.1) 2. f(-0.1) 3. f(1.2)

A: The linear approximation formula is: L(x)=f(a)+f'(a)(x-a)   For f(3.1), x=3.1 and a=3 So the linear…