" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
x→2⁺
dla x = 2
x³-8*x²+20*x-16 = 2³-8*2²+20*2-16 = 0 =>x = 2 pierwiastek równania
3-2*x = 3-2*2 = -1
x³- 8x² + 20x - 16 = (x - 4)(x - 2)²
(3 - 2x) / (x³ - 8x² + 20x - 16) = (3 - 2x) / (x - 4)(x - 2)²
lim [(3-2x)/(x³-8x²+20x-16)] = lim [(3-2x)/(x-4)(x-2)²]
x→2⁺ x→2⁺
dla 2 < x < 2+δ δ -bardzo mała liczbaδ > 0
(3 - 2*x) = -1 - 2δ ≈ -1 < 0
(x - 4)(x - 2)² = (δ - 2)(δ)²= -(2 - δ)(δ)² ≈ -0 < 0
-1/(-0) =+∞
lim [(3-2*x)/(x-4)(x-2)²] = -1/(-0) = +∞
x→2⁺
-------------------------------------------------------------------------------------------
lim [(3 - 2x) / (x³ - 8x² + 20x - 16)] = ?
x→2ˉ
lim [(3 - 2x)/(x³ - 8x² + 20x - 16)] = lim [(3 - 2x) / (x - 4)(x - 2)²]
x→2ˉ x→2ˉ
dla (2-δ) < x < 2 δ -bardzo mała liczbaδ > 0
(3 - 2*x) = -1 + 2δ ≈ -1 < 0
(x - 4)(x - 2)² = -(δ+2)(-δ)² ≈ -0 < 0
-1/(-0) =+∞
lim [(3-2*x)/(x-4)(x-2)²] = -1/(-0) = +∞
x→2ˉ
w załączniku