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Find derivatives of the following functions using differentiation rules:
1. f(x) = 9x+5
2. f(x) = 3e^x
3. f(x) = 3x^3 + 4
4. f(x) = x^4 + 3x^2 + 4x - 31
5. f(x) = (2x + 3)e^x
6. f(x) = (2x - 1)e^(x-3)
7. f(x) = x(x-2)^2 = x(x^2 - 4x + 4) = x^3 - 4x^2 + 4x
A rectangular storage unit has dimensions 1m by 2m by 3m. If each linear dimension is increased by the same amount. What increase would result in a new storage unit with a volume 10 times the original?
Linear Fractional Transformation is a Mapping f: C --> C A fixed point of a transformation is a point z_0 so that f(z_0) = z_0. Show that every linear fractional transformation
Find the linear equation that relates value (V) in dollars to time (t) in years. What would be the value of the equipment after 6 years?
What are examples of variables that follow a binomial probability distribution? What are examples of variables that follow a Poisson distribution?
Find the point P on the line passing through both the origin and the point 1,1,1 that is closest to the point 2,4,4. Then find the point q on the line passing through both the origin and the point 2,4,4
If a and b are positive numbers, what is all the information we can deduce about the relationship between the lines: L1: y = - ax + b and L2: y = (1/a)x + b?
Four people select a main dish from a menu of 7 items. How many choices are possible: If a record is kept of who selected which choice (as a waiter would)
Identify the meaning of independent and dependent events. Calculate probabilities and joint probabilities of simple events. Explain the basic logic of probability theory
Show that the given relations are contradictions
A mini license plate for a toy car must consist of a letter followed by two numbers. Each letter must be a C, A or R. Each number must be a 3 or 7. Repetition of digits is permitted.
Odds and probability, A casino states that the house odds (note: house odds are the odds that the gambler will lose) for a certain game are 23 to 2.
The mean tuition cost at university though the United State is 4260 per year. Use this value as the population mean and assume that population standard deviation is USD 900. Assume that random sample of so university will be selected. What is the pro..
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