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Prove that the indefinite integral from 0->pi/2 of cos^10(x) dx = 9/10 times the indefinite integral from 0->pi/2 of cos^8(x) dx   This problem showed up on one of the old exams...

let 〈xn〉n=1...∞ be a sequence satisfying xn+1=xn-xn-1 for each n. Prove that xn+6=xn for all n belonging to N using the below formula  xn=p((1+i(sqrt3))/2)n+q((1-i(sqrt3))/2)n p...

Given a set A and a set B, one a subset of the other, prove then |A∪B|=[|A|+|B|- (||A|-|B||)]/2   In words: The cardinality of A union B= the cardinality of A plus the cardinality...

Consider the triangle with the vertices: A=(1,2) B=(-1,8) C=(7,10) a. find the midpoint M of Line Segment AB b. find the midpoint N of Line Segment AC c. Verify that Line Segment MN is...

In ΔABC, the points M and N lie 5/8 of the way down the sides on which they lie.    Prove:  i.  Line Segment MN is parallel to the base Line Segment BC ii...

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