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The Limit of a Sequence Posing as a Limit Involving the Number e

Krystian Karczyński 29 April 2024 No Comments

Learn how to solve problems with sequence limits correctly when the number e is involved. The article discusses problems and differences arising from polynomials raised to powers, and when and how to use appropriate formulas for limits with the number e. You’ll also understand how routines in limit calculations can lead to mistakes and how to avoid them.

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Delta equals zero in rational indefinite integrals

Krystian Karczyński 29 April 2024 No Comments

In rational indefinite integrals, there’s often a need to factorize the quadratic trinomial ax^2 + bx + c. We do this using the formula ax^2 + bx + c = a(x – x1)(x – x2), which works when Delta is greater than 0. But what happens when Delta is precisely 0?

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Definite Integrals Calculated with Respect to the Variable y

Krystian Karczyński 22 April 2024 No Comments

Definite integrals can be calculated with respect to variable x or y, and sometimes should be, if it’s more convenient. This often plays a big role in the applications of integrals, such as calculating the areas of regions, arc lengths, volumes, and surface areas of solids of revolution. Often we don’t even have a choice, because the conditions of the problem specify that the curve rotates around the OY axis, not the OX. How do you do that?

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