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Find Tx(x; t) at the points x = - ? /2 and x = ? /2. What do these partial derivatives tell us about the temperature behaviour?
Find the gradient vector of f (x, y). In which direction, (i + 2j) or (2i + j), does f(x, y) change more rapidly? Explain.
Determine if there are separable differential equations among the following ones and explain.
Types of discontinuous functions, finding the domain and range of the discontinuous functions.
The transformation formulas between Cartesian coordinates (x,y) and polar coordinates (r,?) are as follows: x = rcos(?) y = rsin(?)
Determine which of the following expressions represent the exact differential and find the corresponding function satisfying the condition f(-1,2)
Describe the step-by-step process used to determine the function (i.e., amplitude, period, horizontal translation, and vertical translation).
Create a function, f(x), and pick a point c such that the limit of f(x) as x approaches c from the right and the limit of f(x).
What is the number of items that need to be sold in order to make the maximum profit? What is the average cost per item at the maximum profit point?
It is difficult to measure any residual radioactivity if N(t) drops below No/1000. But if this is the case, we can at least say that the living thing.
What is the linear velocity in feet/sec of a point on the rim of the merry-go-round?
Highland Appliance must determine how many color TV's and VCR's should be stocked. It cost highland $300 to purchase a color TV and $200.
Calculate the pH of the solution formed during a titration upon adding 35.0 ml of a standard .150M NaOH solution to.
Starting from alcohol that contains four or less carbon atoms and from benzene and toluene, outline how the following can be synthesized.
Outline all steps in the possible synthesis of each of the following compounds from benzene and / or toluene.
A solution made by dissolving 1.20 g of the unknown compound in 25.0 g of benzene had a freezing point of 4.7 degrees Celsius.
The enantiomers (R and S forms) of the following chiral alcohols need to be separated by a suitable chiral separation method.
Describe the principal structural difference between amylose and cellulose and then between glycogen and cellulose.
Which of the following molecules can hydrogen bond to another of the same compound?
Explain why compound A reacts 9000 times faster than compound B at 0 degrees, but the two compounds react at the same rate at 103 degrees.
When a sample is burned in oxygen, 4.822 g of CO(2) and 1.650g of H(2)O are obtained. What is its simplest formula?
The compound hexane, CH3-CH2-CH2-CH2-CH2-CH3 has how many tertiary hydrogens?
Its optical rotation in sodium line (light wavelenth) was -5.0 degrees at 25 degrees Celsius. What is the specific rotation of the (-)-epinephrine?
The volume occupied by 1 micromole of liquid benzene and the volume occupied by 1 megamole of benzene as a vapor at STP (assume an ideal gas).
Consider the possible isomers of chlorotoluene. Which of the possibilities will result in only two types of aromatic protons by NMR?