Limits and Continuity

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Limits and Continuity

Suppose the functions ƒ(x) and g(x) are defined for all x and that lim (x → 0) ƒ(x) = 1/2 and lim (x → 0) g(x) = √2. Find the limits as x → 0 of the following functions.

e. x + ƒ(x)

Accepted Answer

Welcome back, everyone. Let F of X be a function defined for all X. If limits X approaches 0 of F of X is equal to -1, what is the limit of 2 X plus FXxis X approaches 0? We're given 4 answers chooses A 1, B-1, C3, and D-3. So let's find the limit. We're given limit as x approaches 0 of 2 X plus F of X. Now we can use one of the properties of limits because we have a sum, right? We can essentially distribute the limit for each term. So we're going to get limit as X approaches 0 of 2 X plus limit. As x approaches 0 of F of X. And now we can evaluate each limit separately. So first of all, we have a limit. As x approaches 0 of 2 X, so this is a linear function we can use the right substitution. This gives us 2 multiplied by 0, which is 0. And then for the second limit we have limit as X approaches 0 of F of X, and this is equal to -1. So 0 + 1 gives us -1. And that's it. Using the properties of limits, we have evaluated the final answer which corresponds to the answer choice B-1. Thank you for watching.

Limits and Continuity

Suppose the functions ƒ(x) and g(x) are defined for all x and that lim (x → 0) ƒ(x) = 1/2 and lim (x → 0) g(x) = √2. Find the limits as x → 0 of the following functions.

e. x + ƒ(x)

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Limits and ContinuitySuppose the functions ƒ(x) and g(x) are defined for all x and that lim (x → 0) ƒ(x) = 1/2 and lim (x → 0) g(x) = √2. Find the limits as x → 0 of the following functions.e. x + ƒ(x)

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Limits and Continuity

Suppose the functions ƒ(x) and g(x) are defined for all x and that lim (x → 0) ƒ(x) = 1/2 and lim (x → 0) g(x) = √2. Find the limits as x → 0 of the following functions.

e. x + ƒ(x)