Calculus Answers

Question 9

In a bottle, the height of the liquid is a function of the volume of the liquid in the bottle, say h = 𝑔(𝑣). Similarly, the volume of the liquid is function of the height of the liquid, say 𝑣 = 𝑓(h). Show that 𝑓and 𝑔 are inverse functions.

Question 10

Scientists have developed a radioisotope-based power supply whose power output in watts is

125 given by the following function: 𝑃 = 75𝑒− 𝑡

where t is the number of days the power supply is used. The experimental power supply has been installed in an unmanned undersea vehicle on an exploration mission. The vehicle requires 7watts to operate at full capacity. Use the given information to find the number of days for which the vehicle can operate at full capacity.

Question 6

Classify each of the following functions as algebraic or transcendental.

a) 𝑓(𝑥) = tan(8𝑥)

b) 𝑓(𝑥) = √𝑥5+3 9𝑥+5

c) 𝑓(𝑥) = 9𝑥

d) 𝑓(𝑥) = 1+𝑥

A company that operates for 18 hours a day has introduced a new daily wage system that incorporates variable hourly rate to encourage longer shifts. The company pays $10 for first hour or any part of the first hour. Afterwards, company pays additional 2% per hour for each hour or part of each additional hour. Write a piece-wise function that shows the salary as a function of hours. Also sketch a graph of this function.

Question 8

Describe how the function 𝑓(𝑥) = −(𝑥 + 1)2 − 4 can be graphed using the graph of 𝑦 = 𝑥2 and a sequence of transformations.

Question 2

When two given functions, 𝑓(𝑥) = 𝑥2 + 3 𝑎𝑛𝑑 𝑔(𝑥) = 2𝑥 − 5, are divided with each other, a new third function is obtained. Find (𝑓/𝑔)(𝑥) and identify its domain.

Question 3

A new pizzeria has opened near you home, the owner has decided to offer a 20% discount on the opening day on the pizza whose original price is x dollars. The owner is offering additional 15% discount coupon to those who agree to fill a feedback form afterwards. You and your friends have agreed to provide feedback and thus have become entitled to the additional 15% discount coupon. Use the concept of composite functions to identify the amount that you will pay after applying the coupon on the sale price.

A ball tossed h feet in the air will stay in the air for T= 0: 5p (square root then) h

seconds. Note that when a question uses units the final answer should include appropriate units.

(a) Suppose a ball is tossed 4 feet in the air. When will the ball come down?

(b) If a ball remains in the air for 2.5 seconds, how high was it tossed

laptop manufacturer has estimated that their pro t in thousands of dollars is given by the

expression 6 x 2 + 30 x 10 where x (in thousands) is the number of units produced. What production range will enable the manufacturer to realize a pro t of at least $ 14,000? Be sure to include a concluding statement in the context of the problem

Venue A charges $5,000 to rent their banquet hall for a wedding plus an additional fee of $

69 per guest. Venue B has no hall rental fee but charges $139 per guest for a wedding. Let

g represent the total number of guests for a wedding. Set up and solve an inequality to determine the number of guests you would need to have in order for Venue B to be cheaper than Venue A. Be sure to include a concluding statement in the context of the problem.

A marketing research analyst selects a random sample of ten customers out of the fourty who purchased a particular item from central store. The sample one of ten customers purchased different item from central store i.e. 11, 37, 25, 62, 51, 42, 23, 53,17, 18, 19 11, 32, 20 and the sample of other ten customers purchased different items from central store i.e 5,11,14,7,18,12, 13, 14, 15 16,18,17,16,11. If a random sample of ten items are selected of both customers, what is the probability that customer will have a mean item which is a) at least thirty one b) at most fourty five c) between thirty nine and fifty six d) mean item is fifty percent and e) mean item is hundred percent.

Consider the function "y=\\ ln(1+x)y= ln(1+x)" .

Which of the following is the Maclaurin series expansion of the first three terms?

1. "x-\\frac{x^2}{2}+\\frac{x^3}{6}"
2. "x-\\frac{x^2}{3}+\\frac{x^3}{2}"
3. "x-\\frac{x^2}{2}+\\frac{x^3}{3}"
4. "x+\\frac{x^2}{2}-\\frac{x^3}{3}"

True or False:

The binomial coefficient "\\displaystyle{{-1\/2}\\choose{5}}" is equal to "\\dfrac{63}{256}"