Tính giới hạn limx→−∞8x3+5x2+13−9x2+3x+5+mx.

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§Nếu m=-5 thì limx→−∞8x3+5x2+13−9x2+3x+5−5x

=limx→−∞8x3+5x2+13−2x−9x2+3x+−5+3x

=limx→−∞8x3+5x2+133−(2x)38x3+5x2+132+2x⋅8x3+5x2+13+4x2−9x2+3x−52−3x29x2+3x−5−3x

=limx→−∞8x3+5x2+1−8x38x3+5x2+132+2x⋅8x3+5x2+13+4x2−9x2+3x−5−9x2x⋅9+3x−5x2−3x

=limx→−∞x25+1x2x28+5⋅1x+1x332+28+5⋅1x+1x33+4−x3−5x−x9+3x−5x2+3

=52+4+4+33+3

=1

§ Nếu m<−5 thì limx→−∞8x3+5x2+13−9x2+3x−5+mx

=limx→−∞8x3+5x2+13−2x−9x2+3x−5+3x+(m+5)x

=+∞.

§ Nếu m>-5 thì limx→−∞8x3+5x2+13−9x2+3x−5+mx

=limx→−∞8x3+5x2+13−2x−9x2+3x−5+3x+(m+5)x

lim x đến 3- 3x+2/ x-3 bằng