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Evaluate the limit, if it exists. $\displaystyle \lim_{t \to 1}\frac{t^4 - 1}{t^3 - 1}$

$\frac{4}{3}$

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Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

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To evaluate this limit, we first rewrite teacher the 4th power -1. Overtake U -1. Since direct substitution gives us 1 to the 4th power -1 Over one K -1 which is just 0/0. An indeterminate value notes that T to the 4th power -1 over Take U -1. This is equal to t squared minus one times t squared plus one over T -1 times T squared plus t plus one. Which is the same as T -1 times t plus one times T squared plus one over t minus one times T squared plus t plus one. Now in here we can cancel out the T -1 and reduce the expression into T plus one times T squared plus one over T squared plus t plus one. And so using this we have this limit equal to limit as T approaches one of t plus one times t squared plus one over t squared plus t plus one which is just one plus one times one squared plus one over one squared plus one plus one, which is just 4/3. And so this is the value of the limit.

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Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

Lectures

Join Bootcamp