4. The pdf of X is ƒ (x)=,1

Q: Find the value(s) of C in the given interval that satisfies the mean value Theorem for integral.…

A:

Q: A college professor never finishes his lecture before the end of the hour and always finishes his…

A: c) Given density is, fx=0.375x2, 0≤x≤2 Consider, P30 sec≤X≤90 sec=P0.5 min≤X≤1.5 min)     since, 1…

Q: (0,1). Prove the following functions is uniformly continuous on sin x f(x) =

A: Uniformly Continuous:-  Here we prove the result using a theorem of uniformly continuous.

Q: ´28 – e14z x 0 Determine whether the function f(x) = 14x – 1

A: Solution: Consider the given function is  f(x) = x8-e14x    x<014x-1       x≥0 To check whether…

Q: 3. If f is continuous and f (x) dx = 8, show that the graph of ƒ intersects the line y = 4 at least…

A: The function f is continuous. The integral function is ∫13fxdx=8.

Q: if f(x) is a continuous function at x = -6 * = 0, then a 1- cos4x x2 If f(x)= { a x = 0 r>0 16+Vx-4

A: a= 8.   See the attachment for the complete solution.

Q: 1. Examine the continuity and differential possibilities of function f (x)= |x² – 1| in x= 1.

A: Given To check for continuity at x=1 , we find the limit to the left and right of x=1

Q: 1. Let the function f: R R be given by 1- cos(x) if x + 0, f(x) := if x = 0. 1 Prove that f is…

A: Differentiablity analysis problem....

Q: 16. Suppose that f is differentiable at c and that f'(c) + 0. Show that there exists a ð > 0 such…

A:

Q: 1. Given that x +1 2x2-1 g(x) Show that the g(x) function is continuous at a = 4.

A:

Q: Find the linearization L(x) of the function at a. f(x) = cos(x), a = 77/2 L(x) =

A:

Q: Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0…

A:

Q: Find the Wronskian for the set of functions.{e3x, sin 2x}

A:

Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

Q: Find the absolution extrema of f(x) = (In x)2 on [1, e].

A: We have to determine absolute extrema of girls question

Q: Let $X$ have the pdf $f(x)=4 x^{3}, 0&lt;x&lt;1,$ zero elsewhere. Find the cdf and the pdf of…

A: GivenThe pdf of X is f(x)=4x3                       , 0&lt;x&lt;10                           ,…

Q: 1. Show (in terms of e – 6) that a function f : [2, 7] → R be defined by f(x) = Vx² + 1 is uniformly…

A:

Q: Find the anti-derivative of g(x) = 2*, which contains the point (0, 2.44). ⒸG(x) = -2 O G(x) = 2 O…

A:

Q: Let f(x) = x ln(1+ x*). For all æ € [-1, 1], it is known that In(1 + x) = (-1)" -xn+1 n +1 n=0 2.…

A: Substitute x3 for x in the given power series of ln1+x and simplify.…

Q: Question 8 Show using e, 8 methods that the functions f (x) = 1 and g (x) = sin r %3D 1+ x2 are…

A:

Q: ind the constant k such that f(x) is a PDF over the given interval. f(x) = k(3x2 − x3) on [0, 2]

A:

Q: 2. If f is a continuous function such that S(t)dt = cos(2x)e* - [e s(t)dt for all x, find an…

A:

Q: (3) If the functions f(x) and g(x) are continuous 0sxS1, then f(x)/ g(x) is continuous on the…

A:

Q: Suppose that f (x) has a continuous second derivative f"(x), f(2) = 4, f'(2) = –1, and / f(x) dx =…

A:

Q: 1. Suppose that f : [0, 0) → R is continuous and f(x) # 0 for all x > 0. If we have (f(x))? = 2…

A:

Q: Find "k" so that f(x) is a valid pdf: for x 0 O 16 O 1/2 O 8 O 1/4

A:

Q: 43. If f is differentiable and is periodic with period T, show that f' is also periodic with period…

A: First we prove that f'(x) is periodic by definition of derivative. Then we give an example to prove…

Q: 4. Find the maximum value of f (x) = In(x – In x) on the interval -sse. e

A:

Q: 19.D. Show that the function defined by g(x) g² sin (1/x), x * 0, %3D = 0, 0, is differentiable for…

A:

Q: - if f(x) is a continuous function at x O, then a = 1-cos4x よく0 x? { a If f(x) = r= 0 r>0 V16+ VF -

A: Then to find the value of a if f(x) is continuous at x=0   Since for any continuous function at…

Q: 3. Consider the function g(x) defined by | 22 sin(1/x) if x > 0, g(x) = –x² if x < 0. (a) Show that…

A:

Q: The Second Derivative Test cannot be used to conclude that x = 1 is the location of a relative…

A: Topic:- application of derivatives

Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

A:

Q: 3) Find a value of c for which f(x) is a pdf on the indicated interval. Q11 f(x) =, [0, 1] 1+x2

A: We know that the total probability is always 1. Using that we get:

Q: Find the dérivative of the function: f(x)=In(e^x-13x)

A:

Q: 35. Given that f(z) is a continuous even function, then A 0 D

A: We will use the definition of an even function and properties of definite integrals to find the…

Q: b) Show that the function f (x) = { * x² sin ! for x E (0, 1] for x = 0 is absolutely continuous on…

A:

Q: If Y Poisson(A) and A has pdf f(A) = e-^ for A > 0, elsewhere, find zero E(2Υ) V (2Y):

A:

Q: 6- if f(x) is a continuous function at x = 0, then a = 1- cos 4x x0 V16+ Vx -4 3.

A:

Q: Please see picture

A: Introduction:Here, MX (t) denotes the moment generating function (mgf) of the random variable X;…

Q: If g(g(x)) is continous at 0, then g(x) is continous at 0.  True or False?

A:

Q: Find the global minimum of the function f (x) 1 + x² on the interval (0, co0)

A: Given that f(x)= 1+x2.  And we find global minima on the interval (0, infinity).     Here i attached…

Q: 1 dt, for x > 4. In(t) Let F(x) 4

A:

Q: 15. If f+g is differentiable at a, are f and g necessarily differentiable at a ? If f g and f are…

A: Let f be any function that is not differentiable  at the point a and define as: gx=-fx for all real…

Q: 1. Suppose that g(x) > 0 for all r, g(x) has a continuous derivative, g(-2) = 5 8 g(4) = 3 and |…

A:

Q: 3. Consider the function g(x) defined by { x² sin(1/x) if x > 0, g(x) = if x <0. (a) Show that g(x)…

A:

Q: If f(x)= 2- cos(x) sin(x) , then the absolute minimum of f on the 3T is: interval O 13 O 0 P 2/2-1 O…

A: