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ACTIVITY IN BASIC CALCULUS
QUOTIENT RULE
I. Find the derivative of the following functions below using the quotient rule. Show your complete solution.
- "\\frac{x^2-7x}{2x^3+5x^2}"
- "\\frac{3x^2+7x-14}{x^3-4x^2}"
- "\\frac{2x^3+8x^2}{x^2+6x^2-10}"
II. Create your own given problem involving quotient rule and solve. Show your complete solution. Do not copy the given example below.
1. Example must have two different terms in numerator, and three different terms in denominator
eg. (do not copy)
y= "\\frac{8x^2-3x}{x^2+6x^2-10}"
2. Example must have three different terms in numerator, and three different terms in denominator
eg. (do not copy)
y= "\\frac{x^2+8x^2-3x}{2x^3+6x^2-10}"
A researcher wants to estimate the numbers of hours that 5 years old children spend watching television. A sample of 50 five-year old children was observed to have a mean viewing time of 5 hours. The population is normally distributed with a population standard deviation of 0.5 hours. Find the 95% confidence interval of the population mean.
Given the population 1,3,4,6 and 8. Suppose samples of size 3 are drawn from this population. How many different samples can be drawn from this population?
Customers at the restaurant have to wait an average of 25 minutes before they receive their meal from the time their order was placed. Assume these waiting times are normally distributed with a standard deviation of 5 minutes.
3.1) What is the probability that a randomly selected customer waits between 20 and 35 minutes before receiving his meal from the time his order was placed?
3.2) What is the maximum waiting time for a customer to receive her meal if she is in the 10% of customers who receive their meals in the fastest time from when the order was placed?
Suppose z is a function of x and y, and tan√y2+x2 = zxe6y. Solve for ∂z/∂x and ∂z/∂y.
The lifetime X of an alkaline battery is exponentially distributed with lambda = 0.05 per hour. What are the mean and standard deviation of the battery’s lifetime
Investigating a complaint from a buyer that there is short-weight selling, a manufacturer takes a random sample of twenty-five 32 g cans of coffee from a large shipment and finds that the mean weight is 31 g with a standard deviation of 0.6 g. Is there evidence of short-weighing at the 0.01 level significance?
Determine all the relative minimum and maximum values, and saddle points of the function g defined by g(x,y) = x3 - 3x +3xy2
Show that the function f defined by
f(x,y) = {1, (x,y) = (0,0)
{(x2 + y)/(x + y), (x,y) ≠ (0,0)
is not continuous by using two path test at (0,0).
(dy)/(dx) = - x/(2y)
