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vfvf5vbz
@vfvf5vbz
August 2022
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решите предел: limx-бескон. (1-14x)^2/ ((x-4)^3-(x+4)^3)
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hlopushinairina
Lim(x→∞) (1-14x)²/[(x-4)³-(x+4)³]=∞/∞;
lim(x→∞) (1-28x+196x²)/[(x-4-x-4)((x-4)²+(x-4)(x+4)+(x+4)²]=
=lim(x→∞) (1-28x+196x²)/[(-8)·(x²-8x+16+x²-16+x²+8x+16)]=
=1/(-8) ·lim(x→∞) (1-28x+196x²)/(3x²+16)=
=1/(-8) ·lim(x→∞) [x²(1/x²-28/x+196)]/[x²(3+16/x²)]=
=1/(-8) ·lim(x→∞) (x²/x²)·[(1/x²-28/x+196)/(3+16/x²)]=
=1/(-8) ·196/3=-8.16666
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Answers & Comments
lim(x→∞) (1-28x+196x²)/[(x-4-x-4)((x-4)²+(x-4)(x+4)+(x+4)²]=
=lim(x→∞) (1-28x+196x²)/[(-8)·(x²-8x+16+x²-16+x²+8x+16)]=
=1/(-8) ·lim(x→∞) (1-28x+196x²)/(3x²+16)=
=1/(-8) ·lim(x→∞) [x²(1/x²-28/x+196)]/[x²(3+16/x²)]=
=1/(-8) ·lim(x→∞) (x²/x²)·[(1/x²-28/x+196)/(3+16/x²)]=
=1/(-8) ·196/3=-8.16666