Advertisements
Advertisements
Question
Evaluate the following limits: `lim_(u -> 1)[(u^4 - 1)/(u^3 - 1)]`
Solution
`lim_(u -> 1)[(u^4 - 1)/(u^3 - 1)]`
= `lim_(u -> 1)([(u^4 - 1^4)/(u - 1)])/([(u^3 - 1^3)/(u - 1)]) ...[(because u ->1";" u ≠ 1),(therefore u - 1 ≠ 0)]`
= `(4(1)^2)/(3(1)^2) ...[because lim_(x -> "a") (x^"n" - "a"^"n")/(z - "a") = "na"^("n" - 1)]`
= `4/3`
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 limit:
`lim_(z -> 2) [(z^2 - 5z + 6)/(z^2 - 4)]`
Evaluate the following limit :
`lim_(x -> -3)[(x + 3)/(x^2 + 4x + 3)]`
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)]`
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 -> 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->-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 -> 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)]`
