alexk307 said:Homework Statement
lim h->0 [(11+h)^-1 - 11^-1]/h
Homework Equations
The Attempt at a Solution
I made the numerator into two fractions with the denominator h. After combining the fractions in the numerator I was left with 121 when I put in 0 for h.
Limits of functions with negative exponents refer to the behavior of a function as its input approaches a certain value or infinity, when the function contains negative exponents.
The general rule for finding the limit of a function with a negative exponent is to take the reciprocal of the exponent and evaluate the limit as the exponent approaches infinity.
If the negative exponent is in the numerator, the limit will approach infinity. If the negative exponent is in the denominator, the limit will approach zero.
Yes, a function with negative exponents can have a limit at a specific point if the negative exponent is cancelled out by other terms in the function.
Limits of functions with negative exponents can be used in real-life applications to model exponential decay, such as in radioactive decay or population decline. They can also be used to calculate the half-life of a substance or determine the maximum capacity of a system.