Calculus and statistics

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Question description

Please show all of your work in order to receive full credit. If you are making use of a particular property
or theorem, be sure to state/show that the hypotheses are satis ed. It would be greatly appreciated to complete this in 24 hours.

MET CS 546B HA Homework 4 Due on 6/19 Please show all of your work in order to receive full credit. If you are making use of a particular property or theorem, be sure to state/show that the hypotheses are satisfied. All work must be neatly written (or typeset if you choose to do so) and stapled. 1. For the function f (x) = x3 + 3x2 , find the following: (a) Horizontal or vertical asymptotes, if any. (b) Points of maximum and minimum and the value of the function at these points. (c) Inflections points and the value of the function at those points. (d) Describe the behavior of the graph of the function, using the above information you discovered. 2. Suppose a product code is a string made up of 6 characters. The first 4 characters can each be any of the digits 1-5, and the last two characters can each be any of the alphabet characters A-D. If repetition is allowed (e.g. 11AA is an allowable code), how many different possible such product codes are there? 3. Let the experiment E be picking two cards out of a standard 52-card deck with replacement (i.e. you shuffle, pick one card, and then put that card back in the deck and shuffle again). How many ways can you get a 7 and a 6? 4. Let the experiment E now be picking one card out of a standard 52-card deck. How many ways can you get a 7 or a 6? 5. Let the experiment E be flipping a coin k times in succession. Using k-samples, how many possible outcomes are there of E? 6. How many permutations are there of the word “computer”? Remember, a permutation of an ordered set of n elements is some arrangement of those elements. So we think of “computer” as an ordered set of 8 elements, where the only elements we have are ‘c’,‘o’,‘m’,‘p’,‘u’,‘t’,‘e’, and ‘r’.

Drfranz
School: Cornell University

Attached.

Question 1.
For the function f (x) = x3 + 3x2,

find the following:

(a) Horizontal or vertical asymptotes, if any.
Solution.

Horizontal asymptote.
A line y=K would be the horizontal asymptote of the above function if;
The lim (x3+3x2) =k
x-α
or if f(x)=k where k is a finite number
x-α
hence on calculating the limits
⁘The lim (x3+3x2) =
x-α
limx3=∞

and

lim 3x2 =3lim x2 + ∞ Where ∞=constant

the

x→∞

x→∞

thus, the lim of the equation =∞
thus, there is no Horizontal asymptote
Vertical asymptote.
A line y=K would be the vertical asymptote of the above function if;
The lim (x3+3x2) =∞
x-α
where the denominator is 0
however, the function has no 0 denominator thus there is no vertical asymptote.

(b) Points of maximum and minimum and the value of the function at these points.
Solution.
The maximum point of a function f (x) = x3 + 3x2 should satisfy the ...

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