Find "k" so that f(x) is a valid pdf: for x < 0 f(x) = %3D kxe-4r2 for x > 0 O 16 O 1/2 O 8 O 1/4

Q: Use the first derivatives to find the local exterme of f(x) =x³ -12x on R

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Q: Find S f(x)dx if f(x) = [2 for x<2 [x for xz2

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Q: Consider the following. f(x) = 2x/ 16 – x², [-4, 4]

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Q: dy Find L y = ln (2²+4) + + Icos HIN

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Q: Compute d (x+2) dxx-2,

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Q: For the PMF Px(x) = = 2 x = 1, 3, otherwise. " calculate Var[X].

A: Answer:- Given pmf is  Px(x) = 1/2 , x= 1, 3  Px(x) = 0 , otherwise.  Using formula,  Var[X] = E(x2)…

Q: Suppose that the p.d.f. of X is as given f(x) = 3(1-x)2 for 0<x<1 and 0 otherwise Find the pdf of…

A: If Y=g(X) is the transformation then the PDF of Y is given by; fY(y)=fX(g-1(y))ddyg-1(y)

Q: Let f(x) = 3x+ 4x. Evaluate dy when x=2 and dx=0.1

A: Given that fx=3x2+4x To evaluate dy when x = 2 and dx = 0.1.

Q: Use the three step process to determine if the function f (x) = S2² +1 ifx 2 at r = 2. Your Answer:

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Q: Is the function below continuous at x = -5? f(x)=x3−2x2+5x+1

A: We are to simplify

Q: If F(x)= 27 0<x <3 then pdf f(x): 9. .2 9X II

A: F(X)=x327 , 0&lt;x&lt;3we have to find probability density function.

Q: Differentiate the following function. 6x2 +5 y= x2 +1

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Q: B. Using Change of Variables and Generalized Power Formula, integrate the following: 1. fx (x2 –…

A: Since we have multiple numbers of question and our guideline is solve first question and kindly…

Q: Differentiate the following function. 6x2 +5 y = x2 +1 dx (x² + 1)< dy (x² + 1) • : (6x² + 5) + (6x²…

A: You just need to apply quotient formula in order to solve this.

Q: Evaluate ₁ f (x) dx if ƒ(x) · = O 14 O 12 O 8 06 2x x-1 if x 3

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Q: calculate the value of coth-1(x) when x is greater than 1

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Q: Differentiate the following function. f(x) = - 2 e 4x d (-2e **) =D - 2 e 4*) %3D dx

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Q: Evaluate: 2 (1) (2-3)* dx 1 1 dx x + 5 (2)

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Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: he Monod growth function describes how the rate of reproduction of a population of microorganisms…

A: As given above;  the Monod growth function models the reproduction rate as a function of R by…