Prove this statement (limits and sequences)

[lep11]

Homework Statement

Let lim f(x)=a as x appr. infinity
Let x_n be a sequence so that lim x_n=infinity as n appr. infinity. Prove using definitions that then lim f(x_n)=a as n appr. infinity.

Homework Equations

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The Attempt at a Solution

I have had hard time trying to grasp how to begin with this...

Because lim f(x)=a as x appr. infinity there

 

[mfb]

Because lim f(x)=a as x appr. infinity there

And that is good otherwise the statement would be wrong.

I would try to use the elementary definitions of convergence for the function and the sequence.