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.

e. cos (g(t))

Accepted Answer

Welcome back, everyone. Let KFX be a function defined for all X. If limit of KX access X approaches 3 equals pi divided by 2, what is the limit of sine of KX access X approaches 3? We're given the four answer choices A says -1, B0, C1, and D2. Now for this problem, we're going to use one of the properties. Let's recall that if we have a limit as X approaches A. Of a composite function such as F of G of X, if we have a continuous function, we can simply take the value of the function at the point of the limit. So F of limit as X approaches A of G of X. And in this context, while we're taking sine, it is continuous everywhere, right? It is a periodic function, and now also K of X is defined for all X. So essentially we're going to use this property and we're going to define our limit as X approaches 3 of sign. Of KF X so we can rewrite it as sign of the limit. S X approaches 3 of K of X and we already know that limits X approaches 3 of K X is equal to pi. Divided by 2, so we're simply taking sine of pi divided by 2, which is equal to 1. Therefore, the correct answer to this problem corresponds to the answer choice C1. 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.
e. cos (g(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.e. cos (g(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.
e. cos (g(t))