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Q. What is set theory? Define universal set? Ans. The universe , or universal set , written as U , is the set that contains all elements being considered in a given dis
L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12 R.H.S =c
Example of 3-D Coordinate System Example: Graph x = 3 in R, R 2 and R 3 . Solution In R we consist of a single coordinate system and thus x=3 is a point in a 1-D co
Division basically refers to multiplication of reciprocal. For example a/b is same as a*1/b or we can say, is same as a*b -1 , which is "a" multiplied to the inverse of "b". There
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A painter leans a 10-foot ladder against the house she is to paint. The foot of the ladder is 3 feet from the house. How far above the ground does the ladder touch the house? Appro
Limit Comparison Test Assume that we have two series ∑a n and ∑b n with a n , b n ≥ 0 for all n. Determine, If c is positive (i.e. c > 0 ) and is finite (i.e. c
Suppose that the number of hours Katie spent practicing soccer is represented through x. Michael practiced 4 hours more than 2 times the number of hours that Katie practiced. How l
If X = {a, e, i, o, u} and Y = {a, b, c, d, e}, then what is Y - X ?
Evaluate the following integral. ∫√(x 2 +4x+5) dx Solution: Remind from the Trig Substitution section that to do a trig substitution here we first required to complete t
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