L'H?pital's law, [ln (1+x)]' =1(x+1) [ex-1]' = the denominator derivatives of e x are all1,so they are 65438+ respectively.

lim(x->； 0) ( 1- cosx) /(x^2/2)

= lim(x->； 0) 2 (1-cosx)/x 2 (0/0 numerator and denominator are differentiated respectively)

= lim(x->； 0) 2sinx/(2x)

= 1

1- cosx ~ x^2/2

The essence of infinitesimal:

The sum of 1 and finite infinitesimals is still infinitesimal.

2. The product of finite infinitesimals is still infinitesimal.

3. The product of bounded function and infinitesimal is infinitesimal.

4. Especially the product of a constant and an infinitesimal is also an infinitesimal.

5. The reciprocal of infinitesimal with non-zero constant is infinity, and the reciprocal of infinity is infinitesimal.