The function g (x)= x/(x + 1)². a) Calculate g(x), determine its sign, construct a table with the variations of g, the limits of g at the domain boundaries and in ± ∞. b) Determine the equation of the tangent line to the curve y = g (x) at x = 0. What is the position of the tangent with respect to the curve? (Subtract the 2 equations and study the sign.)
The function g (x)= x/(x + 1)². a) Calculate g(x), determine its sign, construct a table with the variations of g, the limits of g at the domain boundaries and in ± ∞. b) Determine the equation of the tangent line to the curve y = g (x) at x = 0. What is the position of the tangent with respect to the curve? (Subtract the 2 equations and study the sign.)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter1: Functions
Section1.2: Functions Given By Tables
Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...
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Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
The function g (x)= x/(x + 1)².
a) Calculate g(x), determine its sign, construct a table with the variations of g, the limits of g at the domain boundaries and in ± ∞.
b) Determine the equation of the tangent line to the curve y = g (x) at x = 0. What is the position of the tangent with respect to the curve? (Subtract the 2 equations and study the sign.)
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