Q2 a) If the x3, the 3rd term of a series is 3, and x17, the 17th term is -27, state the series.

Find if the series has a common difference.

b) Coolant hose and nozzle design that to be used on CNC machines, has to ensure that adequate coolant is delivered to the cutter/workpiece interface to maintain surface finish and minimise tool wear. The designer of the nozzle is required to design a series of apertures with a minimum diameter of 5 mm and maximum diameter of 20 mm and with 4 intermediate sizes such that they form a non-linear progression. What diameters would you recommend?

Q3 a) Use the Binomial Theorem to expand (3 - x)5.

b) Check the answer you found for question 3a) by using Pascal's Triangle method.

Q4 Use Maclaurin's Series to find the first four non-zero terms of (cosh )

Q5 Using standard power series definitions, state a series for ex. sin x (first three non-zero terms).

Q6 a) Solve 3 sinh  + 2 cosh  = 7

b) In a capacitive circuit, the instantaneous voltage across the capacitor is given by:

v = V(1 - e-t/CR)

where V is the initial supply voltage, R the resistance, C the capacitance and t the time in seconds from the instant of connecting the supply voltage. If V = 200 volts, R = 10000 ohms and C = 20 x 10-6 farads, how long will it be before the instantaneous voltage is 100 volts?

Q7 Find the value of (6a3 + 3)/(2a3 - 5) as n  

This is a set of questions regarding a series, minimization, the binomial theorem, Pascal's triangle, Maclaurin's series, power series, and a capacitative circuit.

... Then we can write 1?p as an infinite geometric series, 1/p=k/(?10?^(p-1)-1)=(k?? 10?^(p-1) )/(1-1??10?^(p-1 ... Then by the Binomial Theorem, we Now suppose have. ...

... x) beyond the first 4 terms of the series expansion given in ... this efficiently we can use the geometric series formula ... of strings we can form equals Binomial(r+k ...

A Series of Probability Questions. ... 2!2!8! 6 6 6 And using binomial probability we ... The probability can be found by using Bayes' Theorem. ...

... 2. Express the following series using sigma notation: a) (1 X 0)/2 + (2 X 1 ... 3. Use the Binomial Theorem to expand the following equation: a) (2p - 3q)^4 b) (2p ...

... express first the given function in a more convenient way: (1) One applies now the formula of the binomial expansion, which is a power series about : (2) which ...

... It insisted him to arrive at the description of Bode's law explaining the distances between the planets, sequence and series, binomial theorem, law of ...

... Use Bayes' theorem to determine P(A3|B1 ... gives detailed steps on solving a series of statistical questions using excel: binomial distribution, normal ...

... This is Bayes' Theorem in its simplest form. ... Typically, a binomial random variable is the number of successes in a series of trials, for example, the ...

... these probabilities remain constant throughout our series of trials ... In the negative binomial random variable, we wait ... 1 p Use the Central Limit Theorem, we can ...

... value of the variable which is predominant in the series. ... to what type of binomial problem would ... The Central Limit Theorem is perhaps the most important result ...