1-variant.
1.Lagranj teoremasi.
2.Quyidagi funksiya uchun Roll teoremasini shartlarini bajarilishini tekshirib ko’ring.
f(x)= -3x+5 x[1,2] .
3. f(x)= funksiya [0,8] segmentda Roll teoremasi shartlarini qanoatlantiradimi?Asoslang.
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2-variant.
1.Koshe teoremasi.
2. f(x)=1- funksiya [-1,1] segmentda Roll teoremasi shartlarini qanoatlantiradimi?Asoslang.
3.Quyidagi funksiya uchun Roll teoremasi shartlarini bajarilishini tekshiring?
f(x) = -x+1 [-1,1] .
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3-variant.
1.Roll teoremasi.
2.Quyidagi funksiya uchun Lagranj teoremasi shartlarini bajarilishini tekshiring.
f(x)=lnx x![](data:image/png;base64,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)
3.Quyidagi fuksiyalar [-2,2] segmentda Jagranj teoremasini shartlarini qanoatlantiradimi?Asoslang.
f(x)= , f(x)=1- .
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4-variant.
1.Ferma teoremasi.
2.Quyidagi funksiya uchun Lagranj teoremasi shartlarini bajarilishini tekshiring.
f(x)=2x- x .
3.[ ; ] segmentda f(x)=sin3x funksiya uchun Jagranj formulasini yozing.
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5-variant.
1.Lagranj teoremasining geometrik ma’nosi.
2. f(x)=1+ (m,n funksiya berilgan. Hosila olmay turib f’(x)=0 tenglama (0;1)intervalda kamida bitta yechimga ega ekanini isbotlang.
3. -3x+c=0 tenglama (0;1) intervalda ikkita har xil yechimga ega emasligini ko’rsating.
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6-variant.
1.Koshi teoremasining geometrik ma’nosi.
2.[a,b] segmentda f(x)=x(1-lnx) funksiya Lagranj formulasini yozing.
3.f(x)=4 +x-2 funksiya [0,2] segmentda aniqlangan.Lagranj formulasidan foydalanib c ni toping.
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