Answered: How do the slopes of the lines tangent…

Math

Calculus

How do the slopes of the lines tangent to the graph of y = tan-1 x behave as x S ∞?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 64E

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Question

How do the slopes of the lines tangent to the graph of y = tan^-1 x behave as x S ∞?

Expert Solution

Step 1

The slope of the line tangent to the graph of $y = \tan^{- 1} (x)$ at a point is the derivative of the function at that point.

Find the derivative of the function $y = \tan^{- 1} (x)$ .

$\begin{array}{rcl} \frac{d y}{d x} & = & \frac{d}{d x} (\tan^{- 1} (x)) \\ = & \frac{1}{x^{2} + 1} \end{array}$

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