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**pickslides** $\displaystyle \lim_{x \to 4} \tan\frac{\pi}{4} = \lim_{ x\to 4} 1 = 1$

This because the function was not a function of x.

In this question if have to determine which function either $\displaystyle x^3+1~,~x<1$ or $\displaystyle x+1~,~x\geq1$ you must substitute 1 into.

The answer is

$\displaystyle \lim_{x \to 1} x+1 = 1+ 1 = 2$

as $\displaystyle x+1~,~x\geq1$ includes 1, as the restriction tells you it is greater and equal to 1.

$\displaystyle x^3+1~,~x<1$ This restriction only wants numbers less than 1. 1 is not less than 1.