高等数学A上册习题解答 至微分中值定理(4)

华中师范大学专用

y²µ {1(üN¼ê{)µ-φ(x)=f(x) f(a) [g(x) g(a)], (x)=f(x) f(a)+[g(x) g(a)]

¦ §

φ (x)=f (x) g (x), (x)=f,(x)+g (x).

Ï |f (x)|<g (x), g (x)<f (x)<g (x),=

φ (x)<0, (x)>0

φ(x)´üN~ ¼ê§ (x)´üNO\¼ê"u´§ x>a §k

φ(x)<φ(a)=0 (x)> (a)=0

=

[g(x) g(a)]<f(x) f(a)<g(x) g(a)

= x>a ,

|f(x) f(a)|<g(x) g(a).

{2(…Ü¥ ½n)µÏ g (x)>|f (x)|≥0¤± x>a ,g(x)>g(a)d…Ü¥ ½n 3 ξ∈(a,x)¦

f (ξ)f(x) f(a)

=g(x) g(a)g(ξ)l §

|f(x) f(a)||f (ξ)|

= <1

g(x) g(a)g(ξ)= x>a ,

|f(x) f(a)|<g(x) g(a).

(0.3)(0.2)

4