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S25_CTMS-25_Elements of Calculus
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Use Newton’s method on to compute when the initial approximation is .
Let be the -th order Taylor polynomial of centered at . What is the smallest value of for which approximates to two decimal places?
The hyperbolic sine is defined by . What is the -th term in the Taylor expansion of around ?
What are the first three non-zero terms in the Taylor series of centred at ?
For which value of does have a point of inflection?
For which values of does have maxima or minima?
For which interval is positive?
What are the maxima and minima of the function ?
An algorithm can calculate the universe partition function (a function one can give to a statistical physicist to find out the secrets of our universe) with a precision level in time . The parameter corresponds to a specific choice of hyperparameters in the algorithm. For a given , which does one need to choose to use the fastest version of the algorithm?
Which side lengths of a rectangle with a perimeter of maximize its area?