Let z=x+ 1.

x=z- 1

f(z)=z- 1+cos(z- 1)

f( 1)= 1- 1+cos( 1- 1)

=0+cos0

= 1

2、B

Xsin 1/x When x→0, x is infinitesimal, while sin 1/x is a bounded function, and the product of infinitesimal and bounded function is infinitesimal.

3、B

Function continuity → function limit exists, which is a necessary condition for function continuity.

4、D

y'=3(x- 1)^2

y"=6(x- 1)

y"=0

6(x- 1)=0

x= 1

y=( 1- 1)^3=0

y " & gt0:x & gt； 1

y " & lt0:x & lt； 1

Therefore, (1, 0) is the inflection point.

17、

( 1) f(x)=2sinxsin(x+π/6)

=cos[(x+π/6)-x]-cos[(x+π/6)+x]

=cosπ/6-cos(2x+π/6)

=√3/2-cos(2x+π/6)

T=2π/2=π

2kπ= & lt； 2x+π/6 & lt； =π+2kπ

-π/6+2kπ= & lt； 2x & lt=5π/6+2kπ

Monotone increasing interval: -π/ 12+kπ =

(2) x∈[0，π/2]

2x+π/6∈[π/6，7π/6]

cos(2x+π/6)∈[- 1，√3/2]

√3/2-cos(2x+π/6)∈[0， 1+√3/2]

Range: [0, 1+√3/2]