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1. Find dx/dt of x= sqrt(1+cot(3t)).
2. f(x)=(x-2)^2*(x+3)^2, find the interval on which the function f(x) is increasing and decreasing. sketch the graph of y=f(x), and identify and local maximum or mininmum and golobal extrema.
3. f(x)= x^2/(x-1) sketch the graph, identify all extrema, inflection points, intercepts, and asymptotes. show concavity and any discontinuities.
4. f(x)= ln(sqrt((9-x^2)/(4+x^2))) apply laws of logarithms to simplify f(x) then find its derivative.
5. Evaluate the integral log3(x)/(2x)
6. Evaluate the integral sinh^6(x)*cosh(x) dx
7. Evaluate the integral x^2 * sin(2x) dx
8. Evaluate the indefinete integral sin^5(x) dx
Important information about Sets, Counting & Probability : Combinations, How many poker hands consist of four clubs and a card of a different suit?
he first three characters of a car license plate number are letter characters. Car license plates can have repeats. For a), remember that the combination "AA" is possible.a) What's the probability of the first three characters being BAZ?
A computer processes jobs on a first-come first-serve basis in a time-sharing environment. The jobs have Poisson arrival rates with an average of six minutes between arrivals.
Find the equation of parabola from the given data - Determine the equation of a parabola with vertex
Based on the parallelogram law, show that the norms ||.||_1 (1-norm) and ||.||_infinity ( infinity or maximum norm) in R^2 are not induced by any inner product.
Prepare a Flexible Budget Gator Divers is a company that provides diving services such as underwater ship repairs to clients in the Tampa Bay area.
Find the equation of the line through the point (-1, 3), having a slope equal to 3/7. Find the equation of the line that passes through the point (2, 3) and which is perpendicular to the line y = -4x + 5.
What is the "rule of 70"? How long would it take for the price level to double if inflation persisted at (a) 2, (b) 5, and (c) 10 percent per year?
Early one morning it began to snow at a constant rate. At 7 AM a snowplow set off to clear a road. By 8 AM it had traveled 2 miles but it took two more hours for the snowplow to go another 2 miles.
Finding the occurrence of the supernova using the information provided in the problem - devise and execute a strategy for finding out when the supernova actually occured, relative to when the chinese astronomers saw the explosion.
Prove that there is a bijection from the open interval (0, 1) to the half-open interval (0, 1].
For what values of k is the origin a hyperbolic equilibrium point of the system ? In this case, classify it as a sink, source or saddle. For what values of k is the origin a Non-hyperbolic equilibrium point of the system ? In this case, determine..
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