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Find the limit.$ \displaystyle \lim_{\theta \to 0} \frac {\sin \theta}{\theta + \tan \theta} $

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00:23

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

Missouri State University

Baylor 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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how to solve this

02:46

it's clear. So when you read here, so we have the limit. State approaching zero. Sign Peeta over Data plus 10 gin. This is equal to when we convert it in terms of sign and co sign Tine over. Data was sign over. Go sign. We multiply both top and bottom by one over data and this gives us the limit. Must date approaches. Zero for a sign of beta. Over. Beta over one plus. Sign the data over. Data Arms one over. Co sign data. This equals the limit. State approaches zero. Signed data over Rita. Well, over the limit. Estate approaches zero. The one plus the limit. State approaches. Ciro. A sign Data over data earns the limit. State approaches zero. Everyone over co sign. You know, we get one over one plus one. Tell us. Excuse me. Multiplied by one over one. And this gives us one, huh?

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