Let xn -> 0 and (yn) be bounded. Prove xnyn -> 0.

Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

Q: draw the plot for the signal vs time for  f(t)=5e^−2t,for −1<t<2 zero otherwise over the domain…

A: In this question, we need to plot the graph of the given function f(t).

Q: A continuous function defined on an open interval (a,b) must have a minimum value. True False

A:

Q: Let f(x) = 6 + V4x – 5. Find f-'(x). f- (x) = for x > 6

A: Given f(x)=6+4x-5 The objective is to find f-1(x).

Q: Without using R or any technology, for what value x does P(X<x) = 0.5? How do you know?

A: Let X ~ N(150, 12) μ=150 σ=12 The standard normal variate is defined as: Z=X-μσ~N(0,1)

Q: Suppose f(x) is continuous on [3, 8] and -5 < f'(x) < 3 for all x in (3, 8). Use the Mean Value…

A:

Q: Suppose f is continuous, positive, decreasing, and concave up on the interval [5, 15]. Compare each…

A: 1) &gt; left sum will be greater than right because function is decreasing 2)  &lt; because…

Q: Suppose that f(x) = βx2 − 3     if x ≤ 2                                βx + 2       if x &gt; 2…

A:

Q: Find the interval(s) wheref (x) =vx+ 2x+6 jis continuous. A) [2, 6] B (-*, *) C) -6, 6] D) [0, -)

A:

Q: Let X ~ N(12, 5). Find the value of x0 such that (a) P(X > x0) = 0.05 (b) P(X x0) = 0.90.

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Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: Let a be a positive constant. Let f(x) = x (Vx +a). Which of the following numbers is\are critical…

A: given function :

Q: What would be an example of a function that is not integrable on [2, 10] and why is it not…

A: Consider a function: y=1x-2……1

Q: What is the minimum value of function y=(x^3) mod 2?

A: We have to find  the minimum value of function y=(x^3) mod 2.We are going to analyze the function y…

Q: Determine if f(x) = x4sin(1/x3) is uniform contuinius in the interval f : (0,∞) --> R

A: Some facts related to uniform continuity of function: A  function f is uniformly continuous on…

Q: What is the minimum value of function y=(x^2) mod 2?

A: The given function is .The aim is to find the minimum value of the function.

Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

Q: The sketch that represents a continuous function, y = f(x), such that: f'(-3)=Ø f(-3) = 5 and A(1) =…

A: The graph of continuous function f(x) is given in the options. The given data of the function f(x)…

Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find (*") dr.

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Q: Let f(x) Find f(-4) = Sx² +5 (5x2 +5 कर x < 1 x ≥ 1

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Q: Use moment generating functions to show that if X3 = X1 + X2, with X1 X3 - X V3 > vı, and X1 and X2…

A: Solution

Q: Find dy of

A: Use the chain rule of differentiation and simplifie the result.

Q: Determine the area, in square units, bounded above by f(x)=−x^2−10x−16 and g(x)=2x+16 and bounded…

A: Given that fx=-x2-10x-16gx=2x + 16 The objective is to find the area of the region which is bounded…

Q: Suppose that f(x) = βx2-3     if x≤2                                   βx+2       if x &gt; 2…

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Q: Find the x>0 which minimizes 2*. Round to one decimal

A:

Q: Show that 2x² + 3x - 5 11x7 ƒ (x) = { is continuous and differentiable at x = 11. x 11

A: Concept If f( x ) is continuous at x = a then limx→a-f( x ) =limx→af( x ) = limx→a+f( x )