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Limits The concept of a limit is fundamental in calculus. Often, we are interested to know the behavior of f(x) as the independent variable x approaches some
Don't count the number of divisions. Do not use asymptotic notation, instead provide exact answers. (i) What is the maximum number of multiplications required to solve a system
2=42gf
6 male students and 3 female students sit around a round table. The probability that no 2 female students sit beside each other can be expressed as a/b, where a and b are coprime p
Determine the centralizer and the order of the conjugacy: 1) Determine the centralizer and the order of the conjugacy class of the matrix [1, 1; 0, 1] in Gl 2 (F 3 ).
Write down the equation of the line which passes through the points (2, -1, 3) and (1, 4, -3). Write all three forms of the equation of the line. Solution To do the above
Exponential and Geometric Model Exponential model y = ab x Take log of both sides log y = log a + log b x log y = log a + xlog b Assume log y = Y and log a
Two circles C(O, r) and C 1 (O 1 , r 1 ) touch each other at P, externally or internally. Construction: join OP and O 1 P . Proof : we know that if two circles touch each
Logarithm Functions : Now let's briefly get the derivatives for logarithms. In this case we will have to start with the following fact regarding functions that are inverses of ea
Vectors This is a quite short section. We will be taking a concise look at vectors and a few of their properties. We will require some of this material in the other section a
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