Advertisements
Advertisements
प्रश्न
Evaluate the following limits: `lim_(y -> 1/2)[(1 - 8y^3)/(y - 4y^3)]`
Advertisements
उत्तर
`lim_(y -> 1/2)[(1 - 8y^3)/(y - 4y^3)]`
= `lim_(y -> 1/2) (1 - 8y^3)/(y(1 - 4y^2)`
= `lim_(y -> 1/2)((1)^3 - (2y)^3)/(y[(1)^2 - (2y)^2]`
= `lim_(y -> 1/2) ((1 - 2y)(1 + 2y + 4y^2))/(y(1 - 2y)(1 + 2y)`
= `lim_(y -> 1/2) (1 + 2y + 4y^2)/(y(1 + 2y)) ....[(because y -> 1/2 "," therefore y ≠ 1/2),(therefore 2y ≠ 1 therefore 2y - 1 ≠ 0),(therefore 1 - 2y ≠0)]`
= `(1 + 2(1/2) + 4(1/2)^2)/(1/2[1 + 2(1/2)]`
= `(1 + 1 + 1)/((1)/(2)(2)`
= 3
APPEARS IN
संबंधित प्रश्न
Evaluate the following limits: `lim_(u -> 1)[(u^4 - 1)/(u^3 - 1)]`
Evaluate the following limits: `lim_(x -> 2)[(x^3 - 4x^2 + 4x)/(x^2 - 1)]`
Evaluate the following limit:
`lim_(x -> - 2)[(x^7 + x^5 + 160)/(x^3 + 8)]`
Evaluate the following limit :
`lim_(x -> -3)[(x + 3)/(x^2 + 4x + 3)]`
Evaluate the following limit :
`lim_(x -> -2) [(-2x - 4)/(x^3 + 2x^2)]`
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 -> 1) [(x^4 - 3x^2 + 2)/(x^3 - 5x^2 + 3x + 1)]`
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 -> 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_(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->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 limits:
`lim_(z→2)[( z^2 - 5 z + 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)[(x^7 + x^5 + 160)/(x^3 + 8)]`
