The actual tracking weight of a stereo cartridge that is set to track at 3 gm on a particular change can be regarded as a continuous r.v. X with pdf Sk{1-(x-3)² } 2

Q: Find the equation of the normal line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

A:

Q: Estimate the instantaneous rate of change of the function f(x)=−x2+4x−4 at x=1 using the average…

A: Consider the given function f(x)=−x2+4x−4

Q: Suppose that Xis a continuous unknown with 5< X< 5 and having PDF denoted fsatisfying f ( x ) = c (…

A: Given: fx=c×25-x2                  -5&lt;x&lt;5

Q: S(r) = In (r² + 2x + 5)

A: SOLUTION-

Q: Suppose that a PDF for a continuous variable X is given by if 0 x)=3/4

A:

Q: Suppose that Xis a continuous unknown with -4< X< 4  having PDF denoted fsatisfying f ( x ) = c (…

A:

Q: If X and Y have joint pdf given by

A: From the given information, fX,Yx,y=2I0,yxI0,1y                =2, 0&lt;x&lt;y, 0&lt;y&lt;1

Q: 1. Show that the function f(x) = 3x + 2 is continuous at (-2, 3). Is it uniformly continuous?

A: As per our guidelines we are mandated to solve only one question at a time please repost the…

Q: Find the linearization of the function F(x)=tan-1(2x)= arctan(2x) at x=0. Then use linearization to…

A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

Q: Find where the function is continuous, but not differentiable..

A: Given,

Q: What is the total change of f(x) if f'(x)= sin(x) from [0, π]? A/

A: Answer: As per guidelines , we can do 1 question at one time , so please post other question…

Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

A:

Q: The fifth-order partial derivative ∂5ƒ/∂x2∂y3 is zero for each of thefollowing functions. To show…

A: The given function is f(x, y)=y2-ysinx-x4.

Q: Find the anti-derivative of g(x) = sec(x) tan(x) which contains the point (TT, 0). O G(x) = -csc(x)…

A: Solution to the anti-derivative can be found by integrating the function.

Q: The error involved in making a certain measurement is a continuous rv X with the following pdf.…

A:

Q: Suppose that f(x) is a continuous function on the interval [0, π]. If f(x)=(sin x)² for 0<x<, then…

A: Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal…

Q: so  by an = 0 ,   does the divergence test apply ?

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Q: The pdf of a continuous RV X is given by f(x) = 3x², where () < x < 1. The median Q2 of X equals

A: Given :-   fx = 3x2                      0&lt;x&lt;1we have to calculate the median   now ,…

Q: Find the absolute minimum and absolute maximum values of f on the given interval. fx) =Dx -In(7x),…

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Q: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

Q: Fill in the blank/s:

A: We have to fill in the blank.

Q: Find the global maximum and global minimum of the function f(x)=sinx−x in the interval [−π,π].

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Q: Express the limit as a definite integral on the given interval. x; In(1 + x3) Ax, [2, 3] lim 3 dx

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Q: Where is Log(z2 + 2) holomorphic (Analytic ) function ?

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Q: Suppose that fis a continuous function and that1. f(x)dx=-1 and L(x)dx = 5, find the value of…

A: suppose that f is continuous function . We have to find the following

Q: Find the absolute extrema of the function on the closed interval. TEX y = tan 16 ), [0, 4] minimum…

A: Given that, The function is y=tanπx16 on the closed interval [0, 4]. To find absolute extrema:…

Q: The average rate of change of fx) = ax' Over the interval osxs1 IS a

A:

Q: Suppose for sume function f we heve its derivative, f'cx) = e*sin(x), on the %3D interval o< x< ar.…

A: fx is a function such that f'x=exsinx on the interval 0&lt;x&lt;2π We have to determine where the…

Q: Find the slope of the tangent line to the graph of f(x) = x· 2e*cos-1t dt at x = 1 Jln x

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Q: question. sf continuous at x = - 3? AY 5- 4- 3- 20 -5 -4 3 -2 -14 123 4 5 -2- -3- -4- -5-

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Q: Consider the following pdf: fx (X) = 0.06x+0.05 0<x < 5 Since it is a continuous pdf, calculations…

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Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

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Q: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

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Q: Let y =sqrt(x + sqrt(8x + 1)). Using only the definition of rate of change in terms of limit,…

A:

Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: Find the slope of the tangent line to the graph of f(x) 2e'cos-1t dt at x = 1. In x = X'

A: Find the slope with the help of derivative of f(x) at x=1 .

Q: Answer the following True or False: For every continuous nonlinear function, you can find a value of…

A: To states whether true or false. For every continuous non linear function, there is a value of x…

Q: F(x) = x · S, 2e' cos-lt dt at x = 1 In x

A:

Q: The general anti-derivative of the function f (x) - In(x) is given by x In( x)+ C Inx)-x+ C x In(x)…

A: The integral (anti derivative) of fx=lnx can be evaluated by using integration by parts. The…

Q: at waht points is the function y= (cosx)/4x continuous? Describe the set of x-values where the…

A: Given: f(x)=cos x4x

Q: Is f continuous at x = 1?

A: The condition of continues function is, limx→a+fa=limx→a-fa=fa   For limit of function from the…

Q: *** Use the first and second derivative to sketch the graph of f(x) = In(x² +1). In particular,…

A:

Q: It appears that f is not differentiable at a = 0. Moreover, the tangent line does not exist at this…

A: yes it is true.

Q: End fz(3) in terms of the joine pdf of X and Y if

A: From the given information, Let, f(x) be the density function of X. f(y) be the density function of…

Q: Find Tn cebtered at x=0 fir akk b for the function f(x) = 1/(1+x) at a=0

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!