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Summation and proof using mathematical Induction.
Suppose that {xn} is a sequence of positive real numbers for which the sum from i=1 to n of (xi)3 = (summation i=1 to n xi )2 for each n>=1. Prove that xn =n for all n>=1.Give a careful and complete proof by induction.
Trigonometric formulas and identities.
Derivative of the natural logarithm by using the fundamental theorem of calculus - Evaluate the derivative of y = ln x. This solution below is not complete.
You have to perform a reliability analysis of the downtime data.
Solve the following equation
Matrice operations
Prove using mathematical induction.
Real time application of perimeter of a circle. To evaluate the distance travelled using the number of rotations.
To make a conjecture about the tangent lines and the graph with the proof of the conjecture - Find the distance between the functions is greatest, and prove your conjecture.
Calculate the compound interest.
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.
The inflection points and global extrema.
Finding the possible length using the law of cosine.
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