Definition 3.3.8 and Definition 3.4.1 in the picture attached (つつて JetDeainition 3•401(なー)that lim fex) =LLet f be deginedon C-o,a) for some oE R,Let L be a real number. We saythe土)holds : ForE>o there existson A> Nco so that for all xeR 17xcN then lfr)-L|メ>ロ tthat limFoj > -o if the Fllanng hilds:numberso that' For ll axEIR,I7 acxcat8 then foe) cE 2. (a) Give an example of function f: R-→ R where lim -0 and lim /(r) -oo. Motivate.z+0+For this problem, you may motivate with a graph.(b) Give an example of funcetion g: R R where lim0 and lim g(r) x. Motivate.I0+For this problem, you may motivate with a graph.(c) Prove by using definition 3.3.8 that if lim p(r).=∞ and lim q(r) x then lim (p(r)+%3Dq(x)) x. (Hint: E = +. )4 cos(2+a)(d) Prove by using Definition 3.4.1 that lim0.

2 (a) To provide the example for the function f:ℝ→ℝwhere limx→∞ 1f(x)=0 and limx→0+ f(x)=-∞here…

2. (a) Give an example of function f: R-→ R where lim = 0 and lim f(r) = -oo. Motivate. r 00 r0+ For this problem, you may motivate with a graph. (b) Give an example of function g R R where lim =0 and lim g(r) = =00. Motivate. T0+ For this problem, you may motivate with a graph. (c) Prove by using definition 3.3.8 that if lim p(r) -∞ and lim q(x) = 0 then lim (p(r)+ q(r)) = 0. (Hint: E = +5 ) (d) Prove by using Definition 3.4.1 that lim 4 cos(r+a) - 0.