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Evaluate the limit, if it exists.

$ \displaystyle \lim_{t \to 0}\left( \frac{1}{t} - \frac{1}{t^2 + t} \right) $

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02:23

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Limits

Derivatives

Missouri State University

University of Nottingham

Idaho State University

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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Evaluate the limit, if it …

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Find the limit (if it exis…

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Evaluate the limit.$$\…

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to find the limit of one over t minus one over t squared plus T as T approaches zero. We first write this into to limit as T approaches zero of one over t minus one over T. Time. Sleepless one. And then from here we can combine the two fractions and we have the limit as T approaches zero of we have a common denominator of tee times deepest one, and the first term of the numerator would be T plus one this minus one. And then simplifying this. We have limit S. T approaches zero of T over tee times T plus one. And here we can cancel out the tea and we have the limit as T approaches zero of one over T plus one. And so evaluating this limit we have 1/0 plus one or that's 1/1 equal to one. Therefore this is the limit value.

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