- #1
Petrus
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$$\lim_{x \to \pi/4} \frac{1-\tan(x)}{\sin(x)-\cos(x)}$$
progress:
I start with rewriting $\tan(x)=\frac{\sin(x)}{\cos(x)}$
progress:
I start with rewriting $\tan(x)=\frac{\sin(x)}{\cos(x)}$
Petrus said:$$\lim_{x \to \pi/4} \frac{1-\tan(x)}{\sin(x)-\cos(x)}$$
progress:
I start with rewriting $\tan(x)=\frac{\sin(x)}{\cos(x)}$
[tex]\lim_{x\to \frac{\pi}{4}} \frac{1-\tan x}{\sin x - \cos x}[/tex]
Petrus said:$$\lim_{x \to \pi/4} \frac{1-\tan(x)}{\sin(x)-\cos(x)}$$
progress:
I start with rewriting $\tan(x)=\frac{\sin(x)}{\cos(x)}$
The limit of the ratio of difference of trigonometric functions at π/4 is equal to 1. This means that as the input value approaches π/4, the ratio of the difference between two trigonometric functions approaches 1.
The limit of the ratio of difference of trigonometric functions at π/4 can be calculated using the L'Hôpital's rule, which states that the limit of a quotient of two functions can be calculated by taking the derivatives of the numerator and denominator and evaluating the limit again.
The limit of the ratio of difference of trigonometric functions at π/4 is important in calculus and trigonometry, as it helps to determine the behavior of trigonometric functions near the point π/4. It can also be used in solving problems involving angles and trigonometric functions.
Yes, the limit of the ratio of difference of trigonometric functions at π/4 can be different for different functions. It depends on the specific trigonometric functions and their behavior near the point π/4.
The limit of the ratio of difference of trigonometric functions at π/4 is related to other trigonometric limits, such as the limit of sine and cosine functions at π/4. It can also be used to solve other limits involving trigonometric functions at this specific point.