Advertisements
Advertisements
Question
Evaluate the following limit :
`lim_(x -> 1) [(x - 2)/(x^2 - x) - 1/(x^3 - 3x^2 + 2x)]`
Solution
`lim_(x -> 1) [(x - 2)/(x^2 - x) - 1/(x^3 - 3x^2 + 2x)]`
= `lim_(x -> 1) [(x - 2)/(x(x - 1)) - 1/(x(x^2 - 3x + 2))]`
= `lim_(x -> 1) [(x - 2)/(x(x - 1)) - 1/(x(x - 1)(x - 2))]`
= `lim_(x -> 1) ((x - 2)^2 - 1^2)/(x(x - 1)(x - 2))`
= `lim_(x -> 1) ((x - 2 + 1)(x - 2 - 1))/(x(x - 1)(x - 2))`
= `lim_(x -> 1) ((x - 1)(x - 3))/(x(x - 1)(x - 2))`
= `lim_(x -> 1) (x - 3)/(x^2 - 2x) ...[(because x -> 1"," x ≠ 1),(therefore x - 1 ≠ 0)]`
= `(lim_(x -> 1) (x - 3))/(lim_(x -> 1)(x^2 - 2x))`
= `(1 - 3)/(1^2 - 2(1))`
= 2.
APPEARS IN
RELATED QUESTIONS
Evaluate the following limits: `lim_(x -> -2)[(-2x - 4)/(x^3 + 2x^2)]`
Evaluate the following limits: `lim_(x -> 2)[(x^3 - 4x^2 + 4x)/(x^2 - 1)]`
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 limit :
`lim_(x -> -3)[(x + 3)/(x^2 + 4x + 3)]`
Evaluate the following limit :
`lim_(y -> 0)[(5y^3 + 8y^2)/(3y^4 - 16y^2)]`
Evaluate the following limit :
`lim_(x -> 3) [(x^2 + 2x - 15)/(x^2 - 5x + 6)]`
Evaluate the following limit :
`lim_(u -> 1) [(u^4 - 1)/(u^3 - 1)]`
Evaluate the following limit :
`lim_(x -> 3) [1/(x - 3) - (9x)/(x^3 - 27)]`
Evaluate the following limit :
`lim_(x -> sqrt(2)) [(x^2 + xsqrt(2) - 4)/(x^2 - 3xsqrt(2) + 4)]`
Evaluate the following limit :
`lim_(x -> 1) [(x^4 - 3x^2 + 2)/(x^3 - 5x^2 + 3x + 1)]`
Evaluate the following limit :
`lim_(x -> 1) [(x + 2)/(x^2 - 5x + 4) + (x - 4)/(3(x^2 - 3x + 2))]`
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 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->-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_(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_(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:
`\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)]`
