Question

1. $lim_{x

ightarrow2}4x$

Explanation:

Step1: Apply limit - constant - multiple rule

The limit of a constant - multiple of a function is the constant times the limit of the function, i.e., $\lim_{x
ightarrow a}cf(x)=c\lim_{x
ightarrow a}f(x)$. Here $c = 4$ and $f(x)=x$, so $\lim_{x
ightarrow 2}4x=4\lim_{x
ightarrow 2}x$.

Step2: Use the basic limit rule $\lim_{x

ightarrow a}x=a$
Since $\lim_{x
ightarrow 2}x = 2$, then $4\lim_{x
ightarrow 2}x=4\times2$.

Step3: Calculate the result

$4\times2 = 8$.

Answer:

$8$