Limits Archives | Page 3 of 3

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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Function Limits Calculator (OUTDATED) + New Calculator

Krystian Karczyński 10 March 2014 No Comments

Announcement Unfortunately, after over 12 years of providing a free function limits calculator, I had to “turn it off”. The calculator was a simple “widget”

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Two types of discontinuity (function limits)

Krystian Karczyński 18 January 2012 No Comments

As we all know (for example from my Limits Course), a function is continuous at the point x0 when the left-side limit of this function at this point is equal to the right-side limit of the function at this point and is equal to the value of the function at this point.

If any of the equality is not satisfied, the function f(x) is not continuous at the point x0, and the point is called a point of discontinuity. In this naming, you can go a step further and DISTINGUISH the points of discontinuity. See how to do it.

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Proving that sinx does not reach a limit as x approaches infinity

Krystian Karczyński 19 September 2010 No Comments

We have a limit of the function as x approaches infinity from the function f(x)=sinx.

We intuitively feel that the above limit does not exist. x’s are getting bigger and bigger, and the sine values are constantly fluctuating between -1 and 1. But how can we formally demonstrate and prove this?

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