Share a solution. ① The numerator and denominator are physical and chemical respectively. Use √ (1+tanx)+√( 1+sinx), √ (1+sin? X)+ 1 is a continuous function. When x=0, its values are all 2.

∴ Original formula =lim(x→0)(tanx-sinx)/(xsin? x)= lim(x→0)secx( 1-cosx)/(xsinx)= lim(x→0)( 1-cosx)/(xsinx).

(2) Apply L'H?pital's law. The original formula = lim (x→ 0) sinx/(sinx+xcosx) = lim (x→ 0)1(1+xcosx/sinx) =1/2.

For reference.

Tsinghua University Publishing House of Korean Calculus Learning Guide has lectures and exercises, and the exercises are also divided into three groups: A, B and C according to your requirements for difficulty, so you can choose them flexibly. Jimidovich Mathematical Analysis Problem Set Publishing House forgot the classic books, so many topics. The concept, methods and skills of Liu Da's mathematics, the calculus part, is not very clear in Tsinghua University Publishing House, and there are still many good questions.

Personally, I think the college advanced mathematics counseling books published by Harbin Institute of Technology Press and South China University of Technology are the best. Because it arranges the questions well. But we learned to count. I don't know why it suits you.

Good luck.