Advertisements
Advertisements
प्रश्न
Evaluate the following limit :
`lim_(x -> 3) [1/(x - 3) - (9x)/(x^3 - 27)]`
उत्तर
`lim_(x -> 3) [1/(x - 3) - (9x)/(x^3 - 27)]`
= `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)(x - 3))/((x - 3)(x^2 + 3x + 9))`
= `lim_(x -> 3) (x - 3)/(x^2 + 3x + 9) ....[(because x -> 3"," x ≠ 3),(therefore x - 3 ≠ 0)]`
= `(lim_(x -> 3) (x - 3))/(lim_(x -> 3) (x^2 + 3x + 9))`
= `(3 - 3)/(3^2 + 3 xx 3 + 9)`
= 0
APPEARS IN
संबंधित प्रश्न
Evaluate the following limits: `lim_(z -> 2) [(z^2 - 5z + 6)/(z^2 - 4)]`
Evaluate the following limits: `lim_(x -> - 3)[(x + 3)/(x^2 + 4x + 3)]`
Evaluate the following limits: `lim_(u -> 1)[(u^4 - 1)/(u^3 - 1)]`
Evaluate the following limit:
`lim_(x -> - 2)[(x^7 + x^5 + 160)/(x^3 + 8)]`
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 -> 3)[(x^2 + 2x - 15)/(x^2 - 5x + 6)]`
Evaluate the following Limits: `lim_(x -> 3)[(x - 3)/(sqrt(x - 2) - sqrt(4 - x))]`
Evaluate the following Limits: `lim_(x -> 4)[(3 - sqrt(5 + x))/(1 - sqrt(5 - x))]`
Evaluate the following limit:
`lim_(z -> 2) [(z^2 - 5z + 6)/(z^2 - 4)]`
Evaluate the following limit :
`lim_(x -> 3) [(x^2 + 2x - 15)/(x^2 - 5x + 6)]`
Evaluate the following limit :
`lim_(x -> 2)[(x^3 - 4x^2 + 4x)/(x^2 - 1)]`
Evaluate the following limit :
`lim_(x -> sqrt(2)) [(x^2 + xsqrt(2) - 4)/(x^2 - 3xsqrt(2) + 4)]`
Evaluate the following limit :
`lim_(y -> 1/2) [(1 - 8y^3)/(y - 4y^3)]`
Evaluate the following limit :
`lim_(x -> 1) [(x - 2)/(x^2 - x) - 1/(x^3 - 3x^2 + 2x)]`
Evaluate the following limit :
`lim_(x -> 1) [(x^4 - 3x^2 + 2)/(x^3 - 5x^2 + 3x + 1)]`
Evaluate the following limit :
`lim_(x -> "a")[1/(x^2 - 3"a"x + 2"a"^2) + 1/(2x^2 - 3"a"x + "a"^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 limits
`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->1)[(x^3 - 1)/(x^2 + 5x - 6)]`
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->1)[(x^3 -1)/(x^2 +5x -6)]`
Evaluate the following limit:
`lim_(z->2)[(z^2 - 5z + 6)/(z^2 - 4)]`
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 -> 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:
`\underset{x->2}{lim} [(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 ->1)[(x^3 - 1)/(x^2 + 5x - 6)]`
