Qube said:Homework Statement
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Homework Equations
The limit definition of a derivative:
[f(x+h)-f(x)]/h as h approaches zero is f'(x)
The Attempt at a Solution
I'm just not understanding the wording of the question. The limit given in the question is indeed equal to g'(x)
since it's set up properly and indeed sec(pi) is -1 and subtracting -1 makes it a positive 1.
The limit definition of derivative is the mathematical formula used to calculate the instantaneous rate of change or slope of a curve at a specific point. It is represented by the following equation:
f'(x) = lim(h→0) (f(x+h) - f(x))/h
The limit definition of derivative is important because it is the basis for understanding and applying the concept of derivatives in calculus. It allows us to find the rate of change at any point on a curve, which is crucial in many scientific and mathematical applications.
To find the slope of a curve using the limit definition of derivative, you first need to plug in the x-value of the point you want to find the slope at into the equation. Then, you take the limit of the equation as h approaches 0. This will give you the slope or rate of change at that specific point.
The h in the limit definition of derivative represents the change in the x-values. It is the distance between the point you want to find the slope at and a nearby point. As this value approaches 0, the slope becomes more accurate and approaches the instantaneous rate of change.
Yes, the limit definition of derivative can be used for any type of function, including polynomial, exponential, trigonometric, and logarithmic functions. It is a general formula that can be applied to any function to find its derivative at a specific point.