Answers to the extreme exercises of advanced mathematics Advanced calculus Volume 1, higher education press, edited by Yao Mengchen, Second Edition, Chapter 1, answers to extreme exercises, 22 questions (21) (25) (30), (21) (1 + 1 / N) to the power of N + m, the limit when n tends to infinity The limit of (25) (SiN x - sin a) / (x-a) when x tends to a The limit of (30) ln (1 + 2x) / tan4x when x tends to zero Question 21 seems wrong I haven't learned the theorem of question 30. I don't know how to write symbols

Answers to the extreme exercises of advanced mathematics Advanced calculus Volume 1, higher education press, edited by Yao Mengchen, Second Edition, Chapter 1, answers to extreme exercises, 22 questions (21) (25) (30), (21) (1 + 1 / N) to the power of N + m, the limit when n tends to infinity The limit of (25) (SiN x - sin a) / (x-a) when x tends to a The limit of (30) ln (1 + 2x) / tan4x when x tends to zero Question 21 seems wrong I haven't learned the theorem of question 30. I don't know how to write symbols

(21) primitive = LIM (n - > ∞) [(1 + 1 / N) ^ (n + m)]
={lim(n->∞)[(1+1/n)^n]}^m
=e^m
(25) original formula = LIM (x - > A) [(SiNx Sina) / (x-a)]
=lim(x->a)[2cos((x+a)/2)sin((x-a)/2)/(x-2)]
=lim(x->a)[cos((x+a)/2)]*lim(x->a)[sin((x-a)/2)/(x-2)/2]
=cosa*1
=cosa
(30) the original formula = LIM (x - > 0) {[2 / (1 + 2x)] / [4sec & sup2; (4x)]} (0 / 0 type, applying Robida's law)
=1/2lim(x->0)[cos²(4x)/(1+2x)]
=1/2*1
=1/2