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MATH 16A WORKSHEET 10-
(1) Suppose x and y are both differentiable functions of t and are related by the equation y4 - x2 = 1. Use implicit differentiation with respect to t to determine dy/dt in terms of x, y, dx/dt .
(2) A tank has the shape of an upside down cone with radius 3 meters and height 4 meters. Water is pouring into the tank at 2 cubic meters per second. How fast is the water level rising when the water level is 3 meters high?
(3) Solve the equation 22x - 2x+2 - 32 = 0 for x.
(4) Find f' and f'' for f(x) = ex2-x. Find the absolute minimum and explain why it is an absolute minimum.
(5) Find the derivative of the following functions.
(a) f(x) = ln √x
(b) f(t) = (ln(e2t + 1))2
(c) f(x) = ln(x ln(x + 1)).
what caption would the automobiles and trucks be reported in the balance sheet of
Suppose a rational function R(x) has the horizontal asymptote y=3/2. Explain the behavior of the function as the variable x increases without bound
Explain the theory in your own words based on the case study and suggested readings. Include the following in your explanation:
Identify the most important things you have learned from the course so far. Then, explain the strategies you have used to learn them.
A mailbox is composed of a prism and a half cylinder. What is the approximate volume of the mailbox?
A class of students opens several bags, counts the various colors of jelly beans, and calculates the proportion that are pink in each bag. Is it appropriate to use a Normal model to describe the distribution of the proportion of pink jelly beans?
question the minute hand on a watch is 8 mm long and the hour hand is 4 mm long. express the square of the distance
How much does Luke need to earn per year (at least) to comfortably afford his repayment if he needs to allocate 12% of his paycheck?
Suppose you are making observations of a system which changes in time and which can be in one of three states. Does entropy have a maximum, minimum or both?
Mean and Variance and Error Probability, Binary data are transmitted over a noisy communications channel in block of 16 binary digits
Compute the expected return and standard deviation for a portfolio formed between M and your choice in part (b). Then compute the weighted-average standard deviation of this portfolio and explain why the portfolio’s actual standard deviation is less ..
Steven has 3 3/4 pounds of pecans and 6 2/3 pounds of walnuts.How many more pounds of walnuts than pecans do Steven have ?
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