Find an equation of the tangent line to the curve y tan ( pie x2 / 4) at the point (1,1) (b) Illustrate part (a) by graphing the curve and the tangentline on the same screen.

Name: Find an equation of the tangent line to the curve y tan ( pie x2 / 4)
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Description: Find an equation of the tangent line to the curve y tan ( pie x2 / 4) at the point (1,1) (b) Illustrate part (a) by graphing the curve and the tangentline on the same screen.

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Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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Find an equation of the tangent line to the curve y tan ( pie x² / 4) at the point (1,1)

(b) Illustrate part (a) by graphing the curve and the tangent
line on the same screen.

Expert Solution

Step 1

To Determine:

Find an equation of the tangent line to the curve y tan ( pie x² / 4) at the point (1,1)

(b) Illustrate part (a) by graphing the curve and the tangent
line on the same screen.

Given: we have $y = \tan (\frac{{πx}^{2}}{4})$ at the point (1,1) .

Explanation:

part a) we have to find the tangent line .

we know that the equation of tangent line is given by

$(y - y_{1}) = m (x - x_{1})$

where m is the slope ,can be written as $m = \frac{d y}{d x}$

now the slope is $m = \frac{d}{d x} (\tan (\frac{{πx}^{2}}{4})) = \frac{πx}{2} s e c^{2} (\frac{{πx}^{2}}{4})$

slope at point (1, 1) is

$m = \frac{πx}{2} s e c^{2} (\frac{{πx}^{2}}{4}) = \frac{π}{2} s e c^{2} (\frac{π}{4}) = \frac{π}{2} {(\sqrt{2})}^{2} = π$

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