Consider the differential equation = t - 2. dt Suppose that y(t) is a solution to this differential equation corresponding to the initial value y(0) = 1. On the graph of y versus t, what is the slope of the tangent line to the curve at the point (0, 1)? Slope = Suppose (instead) that y(t) is a solution to this differential equation corresponding to the initial value y(0) = 5. On the graph of y versus t, what is the slope of the tangent line to the curve at the point (0,5)? Slope = Suppose that y(t) is a solution to this differential equation that passes through the point (678, 172). On the graph of y versus t, what is the slope of the tangent line to the curve at the point (678, 172)? Slope = If we only know the differential equation, (but not any points on the solution curve), which of the following could be a solution to the equation? Select all that apply. A. y = (t - 2)² B. y = ²/2-2t + 172 c.y=t²/2-t D. yt2/2-2t + 1 OE. None of the above Given this differential equation (but not an initial value or the solution) what information is sufficient to determine the slope of the tangent line to the solution curve at a point on the curve? OA. The slope of the solution curve at t = 0. B. The t-coordinate of the point. OC. The y-coordinate of the point. OD. None of the above
Consider the differential equation = t - 2. dt Suppose that y(t) is a solution to this differential equation corresponding to the initial value y(0) = 1. On the graph of y versus t, what is the slope of the tangent line to the curve at the point (0, 1)? Slope = Suppose (instead) that y(t) is a solution to this differential equation corresponding to the initial value y(0) = 5. On the graph of y versus t, what is the slope of the tangent line to the curve at the point (0,5)? Slope = Suppose that y(t) is a solution to this differential equation that passes through the point (678, 172). On the graph of y versus t, what is the slope of the tangent line to the curve at the point (678, 172)? Slope = If we only know the differential equation, (but not any points on the solution curve), which of the following could be a solution to the equation? Select all that apply. A. y = (t - 2)² B. y = ²/2-2t + 172 c.y=t²/2-t D. yt2/2-2t + 1 OE. None of the above Given this differential equation (but not an initial value or the solution) what information is sufficient to determine the slope of the tangent line to the solution curve at a point on the curve? OA. The slope of the solution curve at t = 0. B. The t-coordinate of the point. OC. The y-coordinate of the point. OD. None of the above
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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Transcribed Image Text:Suppose that y(t) is a solution to this differential equation corresponding to the initial value y(0) = 1. On the graph of y versus t, what is the slope of
the tangent line to the curve at the point (0, 1)?
Slope
=
dy
Consider the differential equation = t - 2.
dt
Suppose (instead) that y(t) is a solution to this differential equation corresponding to the initial value y(0) = 5. On the graph of y versus t, what is the
slope of the tangent line to the curve at the point (0,5)?
Slope
=
Suppose that y(t) is a solution to this differential equation that passes through the point (678, 172). On the graph of y versus t, what is the slope of
the tangent line to the curve at the point (678, 172)?
Slope =
If we only know the differential equation, (but not any points on the solution curve), which of the following could be a solution to the equation? Select all
that apply.
OA.y = (t - 2)²
B. y = ²/2 − 2t + 172
c. y = 1²/2-t
OD.y = 1²/2-2t + 1
OE. None of the above
Given this differential equation (but not an initial value or the solution) what information is sufficient to determine the slope of the tangent line to the
solution curve at a point on the curve?
A. The slope of the solution curve at t = 0.
OB. The t-coordinate of the point.
C. The y-coordinate of the point.
D. None of the above
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