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Find the limit.$ \displaystyle \lim_{x \to \pi/4} \frac {1 - \tan x}{\sin x - \cos x} $

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02:15

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

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.

01:22

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he expressed the When you read here we have the limit as X approaches I for it of one minus 10 gin over a sine minus co sign this tangent becomes one minus sign over coastline and when we multiplied the top and bottom by co sign, we get the limits of X approaches. High four one minus sign. That's over. Co sign X over. Sign my guest co sign We want while I co sign, which gives us limit as X approaches by four co sign Linus Stein all over sine minus co sign terms Co sign This becomes equal to the limit as X approaches pi for negative sign Linus Co sign over sine minus co sign find co sign it cancels out to get limit as X approaches high Fours of one over co sign Negative. When we plug in pi forth, we get negative one over co sign of five bars. This becomes really to over two, which gives us an answer of negative route, too

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