Question

encontrar los siguientes limites indeterminados necesito ayuda con estos problemas porfa ​

Answer 1

Si Resolvemos los límites obtenemos que:

• a) Lim x →5 ((x² - 2x - 15)/(x-5)) = 8
• b) Lim x →3 ((x³ - 6x²+9x)/((x-3)²)) = 3
• c)  Lim x →-2 ((x³ + 8)/(x⁴ - 16)) = -0.375
• d)  Lim x →5 ((3x² -13x - 10)/(2x² -7x - 15 )) = 3/2

Resolvemos los limites eliminando la indeterminación:

a) Lim x →5 ((x² - 2x - 15)/(x-5))

=  Lim x →5 (((x-5)*(x+3))/(x-5)) =  Lim x →5 (x + 3) = 5 + 3 = 8

b) Lim x →3 ((x³ - 6x²+9x)/((x-3)²))

= Lim x →3 ((x*(x² - 6x + 9))/((x-3)²)) = Lim x →3 ((x*(x-3)²)/((x-3)²))

= Lim x →3 (x) = 3

c)  Lim x →-2 ((x³ + 8)/(x⁴ - 16))

= Lim x →-2 ((x³ + 2³)/((x²)² - 4²))

=  Lim x →-2 (((x + 2)*(x²- 2x + 4 ))/((x² - 4)*(x² + 4)))

=  Lim x →-2 (((x + 2)*(x²- 2x + 4 ))/((x² - 2²)*(x² + 4)))

=  Lim x →-2 (((x + 2)*(x²- 2x + 4 ))/((x² - 2²)*(x² + 4)))

=  Lim x →-2 (((x + 2)*(x²- 2x + 4 ))/((x - 2)*(x + 2)*(x² + 4)))

=  Lim x →-2 (((x²- 2x + 4 ))/((x - 2)*(x² + 4)))

= ((-2)² - 2*(-2) + 4)/((-2 -2)*((-2)² + 4))

= (4 + 4 + 4)/(-4*(4 + 4)) = 12/-32 = -0.375

d)  Lim x →5 ((3x² -13x - 10)/(2x² -7x - 15 ))  

= Lim x →5 ((3*(x-5)*(x + 2/3))/(2*(x-5)*(x + 2/3)) )

= Lim x →5 3/2 = 3/2