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1. (a) Give an example of a function, f(x), that has an inflection point at (1, 4).
(b) Give an example of a function, g(x), that has a local maximum at ( -3, 3) and a local minimum at (3, -3).
(c) Plot f(x) and g(x) on the same graph being sure to label the inflection point(s) and local extrema.
A sphere and a cube have equal surface areas. Show that the ratio of the volume of the sphere to that of the cube is √6 : √π. Ans: S.A. of sphere = S.A of cube 4π r 2
Newton's Second Law of motion, which recall from the earlier section that can be written as: m(dv/dt) = F (t,v) Here F(t,v) is the sum of forces which act on the object and m
The area of a square is 64 cm 2 . What is the length of one side of the square? To find out the area of a square, you multiply the length of a side through itself, because all
Substitution Rule Mostly integrals are fairly simple and most of the substitutions are quite simple. The problems arise in correctly getting the integral set up for the substi
The length of the diameter of the circle which touches the X axis at the point (1,0) and passes through the point (2,3) is ? Solution) If a circle touches the x-axis, its equatio
Calculate the Probability A bag contains 80 balls of such 20 are red, 25 are blue and 35 are white. A ball is picked at random what is the probability that the ball picked is
Theorem If {a n } is bounded and monotonic then { a n } is convergent. Be cautious to not misuse this theorem. It does not state that if a sequence is not bounded and/or
1) Find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2) Compute the work done by the force ?eld F(x,y,z) = x^2I + y j +y k in moving
Interpretation of the second derivative : Now that we've discover some higher order derivatives we have to probably talk regarding an interpretation of the second derivative. I
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