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O Find an equation of the line which is tangent to f(x) = sin(2x) when r = T/6. O Verify that the point (0, 1) lies on the curve 22 + y + y³ = 2e=Y and compute an equation of the line which is tangent at (0, 1).

O Find an equation of the line which is tangent to f(x) = sin(2x) when r = T/6. O Verify that the point (0, 1) lies on the curve 22 + y + y³ = 2e=Y and compute an equation of the line which is tangent at (0, 1).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
7. (a) Find an equation of the line which is tangent to f(x) = sin(2x) when x = 1/6. (b) Verify that the point (0, 1) lies on the curve r? + y+ y³ = 2e#Y and compute an equation of the line which is tangent at (0, 1). %3D
Transcribed Image Text:7. (a) Find an equation of the line which is tangent to f(x) = sin(2x) when x = 1/6. (b) Verify that the point (0, 1) lies on the curve r? + y+ y³ = 2e#Y and compute an equation of the line which is tangent at (0, 1). %3D
Expert Solution
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.

\large f\left(x\right)=\sin \left(2x\right)

put the given value of x

\large f\left(\frac{\pi }{6}\right)=\sin \left(2\cdot \frac{\pi }{6}\right)

\large f\left(\frac{\pi }{6}\right)= \sin \left(\frac{\pi }{3}\right)

\large f\left(\frac{\pi }{6}\right)= \frac{\sqrt{3}}{2}\quad

the point on the graph is 

\large (x_1,y_1)=\left(\frac{\pi }{6},\frac{\sqrt{3}}{2}\right)

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