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mnzavislan
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Homework Statement
Consider f(x)=x^2.5. Note that limf(x) as x->0+ =0. The input must be less than ___ from 0 to guarantee the output is within 0.1 of the limit.
Homework Equations
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A tolerance limit for a function is a value that represents the maximum distance from the true value of the function at a given point. It is used to measure the accuracy of an approximation.
To find the tolerance limit for a given function, you need to evaluate the function at a certain point and determine the maximum distance between the true value and the approximation. This can be done by using the formula: Tolerance limit =|f(x)-f(a)| where f(x) is the function and f(a) is the approximation at point a.
The tolerance limit for f(x)=x^2.5 near 0 is the maximum distance between the true value of the function and its approximation at the point x=0. This can be calculated by evaluating the function at x=0 and determining the maximum distance from the true value.
Finding the tolerance limit for a given function is important because it allows us to measure the accuracy of our approximation. It helps us determine how close our approximation is to the true value of the function and how much error we can expect in our calculations.
The tolerance limit decreases as the point of evaluation moves closer to the true value of the function. This is because as the distance between the approximation and the true value decreases, the accuracy of the approximation increases, resulting in a smaller tolerance limit.