- #1
Chas3down
- 60
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Homework Statement
(f(x+h) - f(x)) / h
f(x) = 2/x
x = -4
As h approaches 0
Homework Equations
N/A
The Attempt at a Solution
(2/(-4 + h) + 1/2) / h
Don't know where to go from there though, not sure how to simplify.
Chas3down said:Homework Statement
(f(x+h) - f(x)) / h
f(x) = 2/x
x = -4
As h approaches 0
Homework Equations
N/AThe Attempt at a Solution
(2/(-4 + h) + 1/2) / h Don't know where to go from there though, not sure how to simplify.
The limit (f(x+h) - f(x)) / h is used to calculate the instantaneous rate of change of a function at a specific point. It is also known as the derivative of the function at that point.
The limit (f(x+h) - f(x)) / h is calculated by taking the limit as h approaches 0. This means that the value of h gets closer and closer to 0, and the resulting value is the instantaneous rate of change at that specific point.
Yes, the limit (f(x+h) - f(x)) / h is used to find the slope of a curve at a specific point. This slope is also known as the derivative of the function at that point.
The limit (f(x+h) - f(x)) / h is a fundamental concept in calculus as it is used to calculate derivatives, which are essential in determining the rate of change of a function. It is also used to find the slope of a curve, which is crucial in analyzing the behavior of functions.
One limitation of using the limit (f(x+h) - f(x)) / h is that it can only be used for functions that are continuous at the point of interest. If the function has a discontinuity or a sharp turn at that point, the limit cannot be calculated. Additionally, the limit does not exist for some functions, making it impossible to calculate the derivative at that point.