0
y = 3 + 2x - 4x^(2)
dy/dx = 2 - 8x ( The derivative).
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What is the anti-derivative of x squared plus 3?
∫ (x2+3) = ∫x2 + ∫3(1/3)X3 + 3X + C
What is the derivative of 2x plus 3?
2
Limit as x approches -1 of x3 plus x2 plus 3x plus 3 divided by x4 plus x3 plus 2x plus 2?
lim (x3 + x2 + 3x + 3) / (x4 + x3 + 2x + 2)x > -1From the cave of the ancient stone tablets, we cleared away several feet of cobwebs and unearthed"l'Hospital's" rule: If substitution of the limit results in ( 0/0 ), then the limit is equal to the(limit of the derivative of the numerator) divided by (limit of the derivative of the denominator).(3x2 + 2x + 3) / (4x3 + 3x2 + 2) evaluated at (x = -1) is:(3 - 2 + 3) / (-4 + 3 + 2) = 4 / 1 = 1
X2 plus 6x plus 1 equals 0?
x2 + 6x + 1 = 0 x2 + 6x + 9 = 8 (x + 3)2 = 8 x + 3 = ± 2√2 x + 3 = -3 ± 2√2 x ∈ {-3 - 2√2, -3 + 2√2}
Factor x3 plus 2x2 plus 3x plus 6?
x3 + 2x2 + 3x + 6 = x2(x + 2) + 3(x + 2) = (x + 2)(x2 + 3)
