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Find the indicated limit.$$\lim _{t \rightarrow 3} \frac{(t+1)^{2}(t-2)^{7}}{(t+2)^{2}}$$

$16 / 25$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

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Lectures

04:40

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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in this problem, we have to find the in the gathered indicated limit off the given function, which is limit three approaches to three off three plus one whole scare into T minus tree. Also care divided by t plus two. All scared. Here the human rational function is define for de approaches to three. So let us apply the limit as t approaches to three. We have three plus one, all scared into three minus tree. Also care divided by three plus two, all scared. That is simply by three plus one. Four times two is 16 into three. Ministry zero Who's security is also zero. So we have zero upon three plus 25 Scared is 25. So from new military we have zero 1 25. We use zero hands there and acquired limit off The given function is zero

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