Limit Evaluation for (1-tan x) / (sin x - cos x) as x approaches pi/4

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Homework Help Overview

The problem involves evaluating the limit of the expression (1 - tan x) / (sin x - cos x) as x approaches π/4. The subject area pertains to calculus, specifically limits and trigonometric functions.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various approaches, including rewriting tan x as sin x/cos x and considering L'Hopital's Rule due to the indeterminate form 0/0. There is also mention of simplifying the expression and evaluating at the limit point.

Discussion Status

The discussion includes attempts to manipulate the expression and evaluate the limit, with some participants sharing their results and reasoning. There is no explicit consensus on the final outcome, but various methods are being explored.

Contextual Notes

Participants are working within the constraints of the problem as posed, with some uncertainty about the best approach to take. The discussion reflects an ongoing exploration of the limit evaluation without definitive conclusions.

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Homework Statement



lim (1-tan x) / (sin x - cos x)
x-->pi/4

Homework Equations





The Attempt at a Solution



Im not sure where to start with this one. Should I turn tan x into sinx/cos x and try to do cancel some of the equation out?
 
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That might work. Another approach is L'Hopital's Rule if you know it, since this expression has the indeterminate form 0/0.
 
meeklobraca said:

Homework Statement





Im not sure where to start with this one. Should I turn tan x into sinx/cos x and try to do cancel some of the equation out?

I just tried what you suggest and it came out okay.
 
Well I did some work with the equation and got 2/sqrt 2

This is how I got there,

I made the 1 = cos x/cos x
The tan x = sin x/cos x

Then I brought the denomenator up which canceled out both sin x - cos x which left me with 1 / -cos x

I plugged in the pi/4 which is sqrt 2/2 , which equals -2/sqrt2, which equals -sqrt2

What do you guys think?
 
Last edited:

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