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Find the limit.$ \displaystyle \lim_{x\to 0} \frac {\sin - 5x}{3x} $
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00:27
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 3
Derivatives of Trigonometric Functions
Derivatives
Differentiation
Missouri State University
Campbell University
University of Michigan - Ann Arbor
Boston College
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.
44:57
In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
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it's clear. So when you married here. So we're gonna find the limit. As X goes to therapy, we're sign five X over three eggs. So our goal here is charging me five x in the denominator. So we're going to multiply 5/3 times 3/5. This becomes 5/3 limit. Thanks. Approaches. Ciro three sign five X over five times three x and then we could simplify this into five birds limit. So that's approaches. Ciro. Their sign five Lex over five x and we're going to use you. Gonna substitute five x by you, which is equal to 5/3 limit as you approach is Ciro for a sign you over you. So we see that the limit X approaches syrup of sine X over X is equal to one, so it's 5/3 times one is equal to 5/3.
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