x¹ - 1 x→1 x-1 cos(π + h) +1 h 28. (a) lim h→0 29. Find dy/dx/x-1, given that y = 1-x². 30. Find dy/dx/x=-2, given that y = (x + 2)/x. 31. Find an equation for the line that is tangent to the cur graphing y = x³ - 2x +1 at the point (0, 1), and use a graph the curve and its tangent line on the same s (b) lim

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

A: A sequence is bounded if it is bounded above and below, that is to say, if there is a number, k,…

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

A:

Q: Suppose X~N(196,20). Find x such that Pr(X > x) = 0.619.

A: The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the mean…

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: If the SAT score of high-school students X~ N(1500, 100²). Calculate P(X> 1650). Calculate P(1400 <…

A: X ~ N (µ, σ )= N(1500, 100) Mean(µ) = 1500Standard deviations (σ) = 100

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Q: Score: of 11 > Macmillan Learning 59.390 When there are few data, we often fall back on personal…

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Q: X~N(100,9). That is, E(X)=100 and Var(X)=9. Find Prob(60<X<80).

A: Given that  Given that.   X~N( μ , ?^2 )   μ=100    , ?=3   Z-score =( x - μ )/?

Q: Is a function Continuous ?why? integrable anod

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Q: Describe a way of showing that a continuous function on an open interval (a, b) has a minimum value.

A:

Q: Find the area of the region bounded by the graphs of ƒ1x2= 5 - x2 and g1x2= x2 - 3 (as shown).

A: Given fx=5-x2  and gx=x2-3 We have to find the area of bounded region.

Q: What is the area of the region bounded to the right by x = -y²+2 and to the left by x = y²? 5432-…

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Q: Find  limit x 0  1/x^2if it exists.

A: We find the limit numerically

Q: Let i, j ∈ Za and w, x ∈ Zb with i, j different from each other and w, x different from each other.…

A: Say, the total number of elements in Za = m, the total number of elements in Zb = n,  The total…