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1. Differentiate the following functions with respect to x.
(a) Use the quotient rule to differentiate
y= 2x4 - 3x/4x - 1(b) Use the Chain rule to differentiate
y = 6cos(x3 + 3)
(c) Select an appropriate rule to differentiate
y = (4x2 - e2x )sin3x
2. Find the following integrals,
(a) ∫(5x2+√x-4/x2)dx
(b) ∫[cos(x/2)-sin(3x/2]dx
(c) 15∫s/√s2+4ds3. (a) Find the area bounded by the curve y = 1/x between x =2 and x =6. (Give your answer to 3 decimal places.)
(b) Sketch the curve for y = sin(x) between x =0 and x =2Π then find the total area enclosed by the curve y = sin x and the X axis between x=0 and x= 1.7Π
A code consists of 2 different symbols selected from X followed by 3 not necessarily different symbols from Y. How many different codes are possible?
Similarly, one additional unit will be occupied for each 9 dollar decrease in rent. What rent should the manager charge to maximize revenue.
a company car has a seating capacity of 8 is to be used by 8 employees who have formed a car pool. if only 3 of theses employees can drive, how many possible seating arrangements are there for the group?
ill's father bought Jill a car with the understanding that she would pay the car off in four years by making equal monthly installments. The car cost her father $6000 plus 9% sales tax. How much are the monthly payments Jill must make to her fathe..
the probability that she is either rich or beautiful is 0.5, what is the probability that she is both rich AND beautiful?
a. If you press a wooden peg against another piece of wood and spin the peg rapidly, it can become hot enough to ignite. The peg produces thermal energy no matter how fast it spins, so why is it important that it spin rapidly?
the standard deviation of monthly changes in the spot price of live cattle is in cents per pound 1.2. the standard
In a classroom of children (13 boys and 12 girls), five students are chosen to go to the blackboard. What is the probability that no boys are chosen?
A 1400 {rm kg} car traveling at a speed of 40 {rm m/s} skids to a halt on wet concrete where mu_k = 0.30. How long are the skid marks?
assume that y1, y2 are solutions of the equation y''+py+qy=0 where p and q are functions of t.
Use the distributive property to remove the parentheses in the following expression. Then simplify your result if possible.
The lateral area of a rectangular prism with height of 5 feet is 175 feet squared. What is the perimeter of the base?
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