Limits and Continuity

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Limits and Continuity

Suppose that ƒ(t) and ƒ(t) are defined for all t and that lim t → t₀ ƒ(t) = ―7 and lim (t → t₀) g (t) = 0 . Find the limit as t → t₀ of the following functions.

h. 1 / ƒ(t)

Accepted Answer

Welcome back, everyone. Let PF X be a function defined for all X. If limit as X approaches X0 of P X equals 5, what is the limit of 1 divided by PXX approaches X0? We're given 4 answer choices A 5, B-5, C 1/5, and D 15th. So basically we want to define the limit as X approaches X0 of 1 divided by E of X, given the limit as X approaches X0 of E X, right? So for this problem, we want to real one of the properties of limits. Let's suppose that we have a limit as X approaches A and we have a composite function F of G of X. If our function is defined and continuous everywhere, we can essentially take F at a point of the limit as x approaches A of G of X, and this is exactly what we want to do. We can essentially take the reciprocal of the limit, right, or simply speaking, we can distribute the limit and we can say that we're taking limit as x approaches X not of 1. Divided by Limit as x approaches X not of p of X and in our numerator we have a constant function. It's simply 1 so we can rewrite 1 and then in the denominator we have limit as x approaches X not of PX. This is very useful because we know that this limit is equal to 5, so we simply end up with 1 divided by 5, which is 1/5, and this means that the correct answer to this problem corresponds to the answer to is C. 1/5. Thank you for watching.

Limits and Continuity

Suppose that ƒ(t) and ƒ(t) are defined for all t and that lim t → t₀ ƒ(t) = ―7 and lim (t → t₀) g (t) = 0 . Find the limit as t → t₀ of the following functions.
h. 1 / ƒ(t)

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Limits and ContinuitySuppose that ƒ(t) and ƒ(t) are defined for all t and that lim t → t₀ ƒ(t) = ―7 and lim (t → t₀) g (t) = 0 . Find the limit as t → t₀ of the following functions.h. 1 / ƒ(t)

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Limits and Continuity

Suppose that ƒ(t) and ƒ(t) are defined for all t and that lim t → t₀ ƒ(t) = ―7 and lim (t → t₀) g (t) = 0 . Find the limit as t → t₀ of the following functions.
h. 1 / ƒ(t)