Advertisements
Advertisements
Question
Evaluate the following limits: `lim_(x -> 3)[(x^2 + 2x - 15)/(x^2 - 5x + 6)]`
Advertisements
Solution
`lim_(x -> 3)[(x^2 + 2x - 15)/(x^2 - 5x + 6)]`
= `lim_(x -> 3) ((x + 5)(x - 3))/((x - 2)(x - 3)`
= `lim_(x -> 3) (x + 5)/(x - 2) ...[("as" x -> 3"," x ≠ 3),(therefore x - 3 ≠ 0)]`
= `(3 + 5)/(3 - 2)`
= 8
APPEARS IN
RELATED QUESTIONS
Evaluate the following limits: `lim_(z -> 2) [(z^2 - 5z + 6)/(z^2 - 4)]`
Evaluate the following Limits: `lim_(x -> 2)[((x - 2))/(2x^2 - 7x + 6)]`
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_(x -> 3) [(x^2 + 2x - 15)/(x^2 - 5x + 6)]`
Evaluate the following limit :
`lim_(x -> sqrt(2)) [(x^2 + xsqrt(2) - 4)/(x^2 - 3xsqrt(2) + 4)]`
Evaluate the following limit :
`lim_(x -> 2) [(x^3 - 7x + 6)/(x^3 - 7x^2 + 16x - 12)]`
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_(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_(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_(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)]`
