(1) If a(x)-x), a(x)-B(x):

② if a(x)-B(x), then a(x)-B(x):

③ if a(x)-(x), then a(x)-(x)-o(a(x):

④ if a(x)-B(x)-o(a(x), then a(x)-B(x),

The serial number of the true proposition is (

(A)①②

(B)①④

(C)①③④

(D)②③④

Answer D. Analytic income a(x)= 1-cosx, B(x)=. X2, exclude ①, so choose D. 。

3. Let the function f(x) have the second derivative at xx, then (

(a) f (x) > 0 when F (x) monotonically increases in a certain domain of O.

(b) When f (x)>0, f(x) increases monotonically in a certain neighborhood of xo.

(c) when f(x) is a concave function in the neighborhood of xo, (x)>0.

(d) when f "(x) >; 0, f(x) is a concave function in a neighborhood of x.

Answer B.

The analytic factor f(x) has the second derivative at x=x, then

F (x) = LIMF)-F2 exists.

x→0

x-x

x→0

When f' (x) >; 0,3 δ > is derived from the local sign-preserving property of limit. 0, when x∈U(x, δ) has f' (x) >; 0, namely δ > 0,

When x∈U(x, δ), there is f' (x) >; 0, so f(x) monotonically increases in the neighborhood of x=x, while b.