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.PDFcom.neevia.http://www version trial Converter Personal Neevia by Created
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com.neevia.http://www version trial Converter Personal Neevia by Created
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" c Î (a, b) , %
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2. (#$$ %# # + (a, b); |
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3. g(a) = g(b), ) & + / */ / ' (* + ' |
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g (a) = f (a) - |
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a = |
f (a)b - f (a)a - f (b)a + f (a)a |
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f (a)b - f (b)a |
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b - a |
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g (b) = f (b) - |
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- f (b)a + f (a)b |
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# 3 0, $ %#/ g ( + + / * +#/ ! /, * & * ' * 6 * + ) c Î (a, b) /, ) g¢ (c) = 0, *
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f (b) - f (a)
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, %#/ 16 3. 7# * ( 0 ) ##
3. ! % # f g :
1.[a, b];
2.%% # (a, b);
3.g(a) ¹ g(b) g¢ (x) ¹ 0 x Î (a, b).
" c Î (a, b) , %
f ' (c) = f (b) - f (a) . g ' (c) g (b) - g (a)
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h(x) = f (x) - lg (x), |
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3. h(a) = h(b), ) & + / */ / ' (* + ' |
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h(a) = f (a) - |
f (b) - f (a) |
g (a) = |
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g (b) - g (a) |
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h(b) = f (b) - f (b) - f (a) g (b) = f (b)g (b) - f (b)g (a) - f (b)g (b) + f (a)g (b) = |
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g (b) - g (a) |
g (b) - g (a) |
= - f (b)g (a) + f (a)g (b) g (b) - g (a)
# 3 0, $ %#/ h ( + + / * +#/ ! /, * & * ' * 6 * + ) c Î (a, b) /, ) h¢ (c) = 0, *
f ' (c) - f (b) - f (a) g ' (c) = 0, g (b) - g (a)
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4. ! % # f g :
1.%% # d- x0, , , x0;
2.limx® x0f(x) = limx® x0g(x) = 0;
3. g¢ (x) ¹ 0, 0 < |x - x0| < d,
lim f ' (x) = l, x®x0 g ' (x)
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lim f (x) ,
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* # x® x0, 3 c® x0, 1 * 6 * + + * |
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lim |
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x®x0 +0 g (x) |
x®x0 +0 g ' (c) |
c®x0 +0 g ' (c) |
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, %#/ 16 5. .+# , # / ( / 7 #/ 3 * ) 3 7#"
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lim f ' (x) = l. x®x0 g ' (x)
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lim f (x) ,
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. * x1 > x0, |x1 - x0| < d1. !3 ) x Î (x0, x1).
#*. 4. * %#/ +# , # / ( / 7 #/ 3 * ) 3 7#".
%## f # g (#$$ %# ! 0 [x, x1]. limx® x0f(x) = limx® x0g(x) = ¥, f(x) ¹ f(x1) # g(x) ¹ g(x1) # $# *# + x1 # # x, " (/6#"*/ ( * ) 3 #0 x0. 4 ( *)# 1 # * +#/ 2 +! ! # 0 *)
+!3 ( * ) & d1 > 0.
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