Calculus Solutions Ex#1.2

Q.01 Solution: Given that $$\lim_{x \rightarrow a} f(x)=2,$$ $$ \lim_{x \rightarrow a} g(x)=-4$$ $$\lim_{x \rightarrow a} h(x)=0.$$(a) $$\begin{aligned} \lim_{x \rightarrow a}[f(x)+2 g(x)] & =\lim_{x \rightarrow a} f(x)+2 \underset{x \rightarrow a}{\operatorname{lim}} g(x) \\ & =2+2(-4)=2-8=-6 \end{aligned}$$(b) $$\begin{aligned} \lim _{x \rightarrow a}[h(x)-3 g(x)+1] & =\lim_{x \rightarrow a} h(x)-3 \underset{x \rightarrow a}{\operatorname{lim}} g(x)+\underset{x \rightarrow a}{\operatorname{lim}}(1) \\ & =0-3(-4)+1=13 … Read more