1.
\(\lim\left(u_n-2\right)=0\Rightarrow\lim\left(u_n\right)=2\)
2.
\(\lim\left(n+2\right)=+\infty\)
3.
\(\lim\left(u_n+v_n\right)=\lim\left(u_n\right)+\lim\left(v_n\right)=4+2=6\)
4.
\(\lim\dfrac{1}{n+3}=\dfrac{1}{+\infty}=0\)
5.
\(\lim2^n=+\infty\)
6.
\(\lim\left(u_n.v_n\right)=\lim u_n.\lim v_n=2.3=6\)
7.
\(\lim\left(u_n-2\right)=\lim\left(u_n\right)-\lim2=5-2=3\)
8.
\(\lim\limits_{x\rightarrow1}\left[f\left(x\right)+g\left(x\right)\right]=\lim\limits_{x\rightarrow1}f\left(x\right)+\lim\limits_{x\rightarrow1}g\left(x\right)=3+2=5\)
9.
\(\lim\limits_{x\rightarrow1}f\left(x\right)=2\)
10.
\(\lim\limits_{x\rightarrow1}\left(2x+1\right)=2.1+1=3\)
11.
\(\lim\limits_{x\rightarrow0}\sqrt{x+4}=\sqrt{0+4}=2\)
12.
\(\lim\limits_{x\rightarrow+\infty}x^3=+\infty\)
13.
\(\lim\limits_{x\rightarrow1}\left[f\left(x\right).g\left(x\right)\right]=+\infty\)
14.
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