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Actividad 4 calculo diferencial

1. The limit as x approaches 4 of x4-16 is 0. When factored, the expression becomes (x-4)(x+4)(x2+4) which equals 0 as x approaches 4. 2. The limit as x approaches infinity of x7-x2+1 is 1. When factored, the leading terms are x7 for both the top and bottom expressions, which equals 1 as x approaches infinity. 3. The limit as x approaches -1 of x2-1 is 0. When factored, the expression becomes (x+1)(x-1) which equals 0 as the factors are 0 when x is -1.

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Hallar los límites 1. limite x4-16 = X3-8 x 2 (x+2) (x-2) (x2+4) = (2+2 ) (4+4 ) = 32 = 8 (x-2) (x2+2x+4) 4+4+4 12 3 2. limite x7-x2+1 2x7+x3+4 x ∞ x7 - x2 - 1 1 - 1 + 1 x7 x7 x7 = ∞ ∞ = 1-0+0 = 1 2x7+ x3 + 4 2+ 1 + 4 2+0+0 2 X7 x7 x7 ∞ ∞ 3. limite = = x -4 = 4–4 = 0 = 0 x-2 ( 4-2)(2+2) 8 x 4 4. limite x2-1 =(x+1)(x-1) = x+1 = -1+1 = -0 X2+3x+2 (x-2)(x-1) x-2 -1-2 x -1
5. limite 2x2-4x+1 = 3x2+x-2 x +∞ 2x2 - 4x + 1 2 - 4 + 1 2 - 4 + 1 = x2 x2 x2 = x x2 = ∞ ∞ = 2-0+0 = 2 3x2 + x -2 3+ 1 - 2 3 + 1 - 2 3+0-0 3 x2 x2 x2 x x2 ∞ ∞ 6. limite 4x3 - 2x-1 = x2 +x -2 x +∞ 4 x3 - 2x - 1 4 -2 + 1 4 -2 + 1 = x3 x3 x3 = x2 x3 = +∞ +∞ = 4-0+0 = 4 = ∞ x2 + x -2 1+ 1 - 2 1 + 1 - 2 0+0 -0 0 x3 x3 x3 x x2 x3 + ∞ +∞ +∞