Advertisements
Advertisements
Question
Evaluate the following limit :
`lim_(y -> 0)[(5y^3 + 8y^2)/(3y^4 - 16y^2)]`
Solution
`lim_(y -> 0)(5y^3 + 8y^2)/(3y^4 - 16y^2)`
= `lim_(y -> 0) (y^2(5y + 8))/(y^2(3y^2 - 16))`
= `lim_(y -> 0) (5y + 8)/(3y^2 - 16) ...[(because y -> 0"," y ≠ 0),(therefore y^2 ≠ 0)]`
= `(lim_(y -> 0) (5y + 8))/(lim_(y -> 0) (3y^2 - 16))`
= `(5 xx 0 + 8)/(3 xx 0 - 16)`
= `-1/2`.
APPEARS IN
RELATED QUESTIONS
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_(y -> 0)[(5y^3 + 8y^2)/(3y^4 - 16y^2)]`
Evaluate the following limits: `lim_(x -> -2)[(-2x - 4)/(x^3 + 2x^2)]`
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 limit:
`lim_(x -> 1)[(x^3 - 1)/(x^2 + 5x - 6)]`
Evaluate the following Limits: `lim_(x -> 4)[(3 - sqrt(5 + x))/(1 - sqrt(5 - x))]`
Evaluate the following limit :
`lim_(x -> -3)[(x + 3)/(x^2 + 4x + 3)]`
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)]`
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 -> 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->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->-2)[(x^7+x^5+160)/(x^3+8)]`
Evaluate the following limits:
`lim_(z→2)[( z^2 - 5 z + 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) [(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 ->1)[(x^3 - 1)/(x^2 + 5x - 6)]`
