Advertisements
Advertisements
प्रश्न
Evaluate the following limits: `lim_(x -> 3) [1/(x - 3) - (9x)/(x^3 - 27)]`
Advertisements
उत्तर
`lim_(x -> 3) [1/(x - 3) - (9x)/(x^3 - 27)]`
= `lim_(x -> 3)[1/(x - 3) - (9x)/(x^3 - 3^3)]`
= `lim_(x -> 3)[1/(x - 3) - (9x)/((x - 3)(x^2 + 3x + 9))]`
= `lim_(x -> 3)[(x^2 + 3x + 9 - 9x)/((x - 3)(x^2 + 3x + 9))]`
= `lim_(x -> 3)[(x^2 - 6x + 9)/((x - 3)(x^2 + 3x + 9))]`
= `lim_(x -> 3)[(x - 3)^2/((x - 3)(x^2 + 3x + 9))]`
= `lim_(x -> 3)[(x - 3)/(x^2 + 3x + 9)] ...[(because x ->3"," x ≠ 3),(therefore x - 3 ≠ 0)]`
= `(3 - 3)/((3)^2 + 3(3) + 9)`
= `0/27`
= 0
APPEARS IN
संबंधित प्रश्न
Evaluate the following limits: `lim_(z -> 2) [(z^2 - 5z + 6)/(z^2 - 4)]`
Evaluate the following limit:
`lim_(x -> - 2)[(x^7 + x^5 + 160)/(x^3 + 8)]`
Evaluate the following limits: `lim_(y -> 1/2)[(1 - 8y^3)/(y - 4y^3)]`
Evaluate the following limits: `lim_("v" -> sqrt(2))[("v"^2 + "v"sqrt(2) - 4)/("v"^2 - 3"v"sqrt(2) + 4)]`
Evaluate the following limit :
`lim_(x -> 3) [(x^2 + 2x - 15)/(x^2 - 5x + 6)]`
Evaluate the following limit :
`lim_(u -> 1) [(u^4 - 1)/(u^3 - 1)]`
Evaluate the following limit :
`lim_(x -> 3) [1/(x - 3) - (9x)/(x^3 - 27)]`
Evaluate the following limit :
`lim_(Deltax -> 0) [((x + Deltax)^2 - 2(x + Deltax) + 1 - (x^2 - 2x + 1))/(Deltax)]`
Evaluate the following limit :
`lim_(x -> 2) [(x^3 - 7x + 6)/(x^3 - 7x^2 + 16x - 12)]`
Evaluate the following limit :
`lim_(x -> 1) [(x + 2)/(x^2 - 5x + 4) + (x - 4)/(3(x^2 - 3x + 2))]`
Select the correct answer from the given alternatives.
`lim_(x -> -2)((x^7 + 128)/(x^3 + 8))` =
Select the correct answer from the given alternatives.
`lim_(x -> 5) ((sqrt(x + 4) - 3)/(sqrt(3x - 11) - 2))` =
Evaluate the following limit :
`lim_("x" -> -2) [("x"^7 + "x"^5 + 160)/("x"^3 +8)]`
Evaluate the following Limit.
`lim_(x -> 1)[(x^3 - 1)/(x^2 + 5x - 6)]`
Evaluate the following limit:
`lim_(x-> -2) [(x^7 + x^5 + 160)/(x^3 + 8)]`
Evaluate the following limit:
`lim_(z->2)[(z^2 - 5z + 6)/(z^2 - 4)]`
Evaluate the following limit:
`lim_(x->-2) [(x^7 + x^5 +160)/(x^3 + 8)]`
Evaluate the following Limit.
`lim_(x -> 1)[(x^3 - 1)/(x^2 + 5x - 6)]`
Evaluate the following limit:
`lim_(x->2) [(z^2 - 5_z + 6)/ (z^2 - 4)]`
Evaluate the following limit:
`lim_(x ->1)[(x^3 - 1)/(x^2 + 5x - 6)]`
