Pluie

write a power series for e^(2x) -1

find the power series for f ' (x) by a method other than taking the derivative

write an expression for f ' (0.5) in sigma notation

List five sources of variation within a population.

(b) Use the proof of the Integral Test to show that:

ln(n+1) <= 1 + 1/2 + 1/3 + 1/4 + ... + 1/n <= 1 + ln n

(c) use part (b) to determine how many terms M you would need so that: (summation of n = 1 to M) of 1/n > 50

Function may be divergent.

limit as h approaches 0 of [e^(x+h) - e^x] / h

please show work. thanks

The balance wheel of a mechanical watch governs the frequency with which the watch ticks. A wheel cut from a single piece of metal will expand upon heating, thus increasing its moment of inertia. Will this cause the watch to speed up or slow down?

limit (as x approaches 0) of (sin 2x)/(sin 3x)

limit (as x approaches 0) of [ x (cot^2 x)] / [(csc x) +1]

1. A = (i) and B = (j). For A • B

a. What is its magnitude? (I think the answer is 0)

b. What its its direction? (I think the answer is none)

2. Show that i x j = -j x i

Is it just k = k?

3. Justify as to whether or not there can be a vector perpendicular to A x B. A = (3i + 2j) and B = (-3i - 2j).

4. For A = (-2i - 4j), B = (-i + j -k) and C= (4i + 2k). What is A • B • C? (I believe that answer is undefined?)

In an experiment it was found that the total charge on an oil drop was 5.93 x 10 ^ -18 C. How many negative charges does the drop contain?

I know the answer is 37, but what equation do I use or how would I get the answer?

When mixtures of gaseous H2 and gaseous Cl2 react, a product forms that has the same properties regardless of the relative amounts of H2 and Cl2 used.

a. How is this result interpreted in terms of the law of definite proportion?

b. When a volume of H2 reacts with an equal volume of Cl2 at the same temperature and pressure, what volume of product having the saformula HCL is formed?

Tissue microarrays are made in a manner that is most similar to:

A. DNA microarrays

B. Immunohistochemistry slides

C. ELISAs

D. Southern blots

Trypsin digestion cleaves peptides at __________________ residues.

A. Tryptophan

B. Glycine

C. Glutamate

D. Cysteine

Which is the best method for measuring post-translational modifications of proteins?

A. Yeast two-hybrid systems

B. X-ray crystallography

C. NMR

D. Mass spectrometry

Of the following methods, which is not commonly used for determining protein-protein interactions?

A. X-ray crystallography

B. Yeast two-hybrid systems

C. Phage display

D. Suppressor mutation

pleas list your sources

Is protein structure or function more amenable to determination using in silico methods? Why? Please list and describe at least one in silico method used to determine protein structure? Please list and describe at least one in silico method used to determine protein function?

1. Why is very unlikely for a food chain to be more than 10 "links" long?

2. In what trophic level do humans belong? Use proper biology vocab to support your answer.

3. How does biomass, the total amount of living tissue, change as you go up the energy pyramid? Provide a reason for this change.

I know the first cells were prokaryotic.

Please list your source if you used an internet source. I have not found the answer after 20 min. of searching.