Master the Trig Limits: A Comprehensive Guide for Calculus and Mathematical Analysis

Special trig limits

Lim (x -> 0) (sinx/x) = 1Lim (x -> 0) (1 – cosx)/x = 0

There are several special trig limits that are frequently used in calculus and mathematical analysis. These limits involve trigonometric functions such as sine, cosine, tangent, and cotangent.

1. Limit of sin(x)/x as x approaches 0:
The limit of sin(x)/x as x approaches 0 is equal to 1. This limit is often used in the evaluation of various integrals and in the development of the theory of Fourier series.

2. Limit of (1-cos(x))/x as x approaches 0:
The limit of (1-cos(x))/x as x approaches 0 is also equal to 1. This limit is frequently used in conjunction with the previous limit to evaluate various limits and integrals.

3. Limit of tan(x)/x as x approaches 0:
The limit of tan(x)/x as x approaches 0 is equal to 1. This limit is used in evaluating various limits and integrals involving tangent functions.

4. Limit of cot(x)/x as x approaches 0:
The limit of cot(x)/x as x approaches 0 is also equal to 1. This limit is used in evaluating various limits and integrals involving cotangent functions.

5. Limit of sin(x)/cos(x) as x approaches infinity or negative infinity:
The limit of sin(x)/cos(x) as x approaches infinity or negative infinity is undefined or does not exist. This limit is used in evaluating the behavior of function as the independent variable approaches infinity.

6. Limit of tan(x) as x approaches pi/2 or 3π/2:
The limit of tan(x) as x approaches pi/2 or 3π/2 does not exist, or it is infinite. This limit is used in evaluating the behavior of tangent function in its undefined points.

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