User:JORGEMARIOMEDINAMARTIN

1)Derivar:
 * $$\ y(x)=3x^3-4x^2+5x+16$$
 * $$\ y'(x)=9x^2-8x+5+0$$
 * $$\ y'(x)=9x^2-8x+5$$

JORGE MARIO MEDINA MARTIN 5:10, 13 Jul 2004

2)Hallar el limite:
 * $$\lim_{x\to 1}\frac {x^2-1}{x-1}$$
 * $$\lim_{x\to 1}\frac {(x+1)(x-1)}{x-1}$$
 * $$\lim_{x\to 1}{x+1}$$
 * $$\lim_{x\to 1}{1+1}$$
 * $$\ 2$$

JORGE MARIO MEDINA MARTIN 5:10, 13 Jul 2004

3)Hallar el limite:
 * $$\lim_{x\to 1}\frac {2x^2-5x-3}{x-3}$$
 * $$\lim_{x\to 3}\frac {(2x+1)(x-3)}{(x-3)}$$
 * $$\lim_{x\to 3}{2x+1}$$
 * $$\lim_{x\to 3}{2(3)+1}$$
 * $$\lim_{x\to 3}{6+1}$$
 * $$\ 7$$

JORGE MARIO MEDINA MARTIN 5:10, 13 Jul 2004

4)Con la formula de derivada en limite halle:
 * $$\lim_{h\to 0}{2x^2}$$
 * $$\lim_{h\to 0}\frac {2(x+h)^2-2x^2}{h}$$
 * $$\lim_{h\to 0}\frac {2(x^2+2xh+h^2)-2x^2}{h}$$
 * $$\lim_{h\to 0}\frac {2x^2+4xh+2h^2)-2x^2}{h}$$
 * $$\lim_{h\to 0}\frac {2x^2+4xh+2h^2-2x^2}{h}$$
 * $$\lim_{h\to 0}\frac {4xh+2h^2}{h}$$
 * $$\lim_{h\to 0}\frac {h(4x+2h)}{h}$$
 * $$\lim_{h\to 0} {4x+2h}$$
 * $$\ 4x$$

JORGE MARIO MEDINA MARTIN 5:10, 13 Jul 2004

5)Con la formula de derivada en limite halle:
 * $$\lim_{h\to 0}{senx}$$
 * $$\lim_{h\to 0}\frac {sen(x+h)-senx}{h}$$
 * $$\lim_{h\to 0}\frac {(senxcosh+senhcosx)-senx}{h}$$
 * $$\lim_{h\to 0}\frac {senx(cosh-1)+senhcosx}{h}$$
 * $$\lim_{h\to 0}\frac {senx(cosh-1)}{h} + \frac {senhcosx}{h}$$
 * $$\lim_{h\to 0}senx \frac{(cosh-1)}{h} + cosx \frac{senh}{h}$$
 * $$\lim_{h\to 0}senx(0)+ cosx (1)$$
 * $$\ cosx$$

JORGE MARIO MEDINA MARTIN 5:10, 13 Jul 2004

6)Con la formula de derivada en limite halle:
 * $$\lim_{h\to 0}{12x^2-6x+6}$$
 * $$\lim_{h\to 0}\frac {(12(x+h)^2-6(x+h)+6)-(12x^2-6x+6)}{h}$$
 * $$\lim_{h\to 0}\frac {(12(x^2+2xh+h^2)-6x-6h+6-12x^2+6x-6}{h}$$
 * $$\lim_{h\to 0}\frac {12x^2+24xh+12h^2-6x-6h+6-12x^2+6x-6}{h}$$
 * $$\lim_{h\to 0}\frac {24xh+12h^2-6h}{h}$$
 * $$\lim_{h\to 0}\frac {h(24x+12h-6)}{h}$$
 * $$\lim_{h\to 0}{24x+12h-6}$$
 * $$\ 24x-6$$

JORGE MARIO MEDINA MARTIN 5:10, 13 Jul 2004

7)Hallar las derivadas en su maxima expresion de:
 * $$\ y =x^4-x^3+3x^2$$
 * $$\ y''=4x^3-3x^2+6x$$
 * $$\ y'''=12x^2-6x+6$$
 * $$\ y=24x-6$$
 * $$\ y'=24$$
 * $$\ y=0$$

JORGE MARIO MEDINA MARTIN 5:10, 13 Jul 2004

8)Hallar la derivada de:
 * $$\ y = \frac {x^4-1}{x^2}$$
 * $$\ y' = \frac {(x^2)(4x^3)-(4x^3-1)(2x)}{(x^2)^2}$$
 * $$\ y' = \frac {(4x^5)-(8x^4-2x)}{(x^2)^2}$$
 * $$\ y' = \frac {4x^5-8x^4+2x}{x^4}$$

JORGE MARIO MEDINA MARTIN 5:10, 13 Jul 2004

100)$$\lim_{x\to 1}\frac {\sqrt[2]x-1}{\sqrt[3]x-1}$$
 * $$\lim_{x\to 1}\frac{(\sqrt[2]x-1)(\sqrt[2]x+1)}{(\sqrt[3]x-1)(\sqrt[2]x+1)}$$
 * $$\lim_{x\to 1}\frac{(\sqrt[2]x)^2-(1)^2}{(\sqrt[3]x-1)(\sqrt[2]x+1)}$$