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7) Find the equation of the tangent line to the curve for y = 2 sin(x) at (,1).

7) Find the equation of the tangent line to the curve for y = 2 sin(x) at (,1).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7) Find the equation of the tangent line to the curve for y = 2 sin(x) at (,1). 8) Suppose a spherical balloon is inflated at a rate of 100 cm³ per minute. How fast is the radius of the balloon increasing when the radius is 1 cm? Note that the volume (V) of a sphere is r³ where r is the radius. dy 9) Consider the equation x² + y² = 3xy - 4. Find evaluated at the point (2,4). dx 10) The position (s) of a particle is given by the equation: 1 s = f(t)= t³-2t² + 3 where t is measured in seconds and s in meters. Note: A positive velocity of a particle (moving in a straight line along x axis) indicates that the particle is moving to the right. (a) Find the position of the particle after 2 seconds. (b) Find the velocity of the particle after 4 seconds. (c) Find the acceleration of the particle after 5 seconds. (d) When is the particle at rest? (e) When is the velocity negative (moving to the left)?
Transcribed Image Text:7) Find the equation of the tangent line to the curve for y = 2 sin(x) at (,1). 8) Suppose a spherical balloon is inflated at a rate of 100 cm³ per minute. How fast is the radius of the balloon increasing when the radius is 1 cm? Note that the volume (V) of a sphere is r³ where r is the radius. dy 9) Consider the equation x² + y² = 3xy - 4. Find evaluated at the point (2,4). dx 10) The position (s) of a particle is given by the equation: 1 s = f(t)= t³-2t² + 3 where t is measured in seconds and s in meters. Note: A positive velocity of a particle (moving in a straight line along x axis) indicates that the particle is moving to the right. (a) Find the position of the particle after 2 seconds. (b) Find the velocity of the particle after 4 seconds. (c) Find the acceleration of the particle after 5 seconds. (d) When is the particle at rest? (e) When is the velocity negative (moving to the left)?
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