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