Q4, We say that function : has the limit in infinity (i.e., when ), if for any (as small as you want) proximity term >0 there exists x, s.t., for any x > x, we have ()<.

(a) What is the limit of increasing function ()=152, when ?

(b) What is the limit of decreasing function ()=+, when , ,, and ,>0?

(c) Propose x for function (), for =110.

(d) Propose x for function (), for =, s.t., >0.

(e) What is the limit of ()(), when ?

Q5, Answer questions about the following functions.

(a) Is function 1()=1 continuous in point =1?

(b) Does 2()=1422 have two-sided limit in point =0?

(c) Is function 3()=14212x continuous in the interval (12,)?

(d) How many discontinuity points has function 4()=2++1(2100), for all ?

(e) How many discontinuity points has function tan()+cot(), for (0,2)?