Advertisements
Advertisements
Question
Evaluate the following limit :
`lim_(Deltax -> 0) [((x + Deltax)^2 - 2(x + Deltax) + 1 - (x^2 - 2x + 1))/(Deltax)]`
Advertisements
Solution
`lim_(Deltax -> 0) ((x + Deltax)^2 - 2(x + Deltax) + 1 - (x^2 - 2x + 1))/(Deltax)`
= `lim_(Deltax -> 0) (x^2 + 2xDeltax + (Deltax)^2 - 2x - 2Deltax + 1 - x^2 + 2x - 1)/(Deltax)`
= `lim_(Deltax -> 0) (2xDeltax + (Deltax)^2 - 2Deltax)/(Deltax)`
= `lim_(Deltax -> 0) (Deltax[2x + Deltax - 2])/(Deltax)`
= `lim_(Deltax -> 0) [2x + Deltax - 2]` ...[∵ Δx → 0 ∴ Δx ≠ 0]
= 2x + 0 – 2
= 2x – 2
APPEARS IN
RELATED QUESTIONS
Evaluate the following limits: `lim_(y -> 0)[(5y^3 + 8y^2)/(3y^4 - 16y^2)]`
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 limits: `lim_(y -> 1/2)[(1 - 8y^3)/(y - 4y^3)]`
Evaluate the following Limits: `lim_(x -> 2)[((x - 2))/(2x^2 - 7x + 6)]`
Evaluate the following Limits: `lim_(x -> 3)[(x - 3)/(sqrt(x - 2) - sqrt(4 - x))]`
Evaluate the following Limits: `lim_(x -> 4)[(3 - sqrt(5 + x))/(1 - sqrt(5 - x))]`
Evaluate the following limit :
`lim_(y -> 0)[(5y^3 + 8y^2)/(3y^4 - 16y^2)]`
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_(x -> 2) [(x^3 - 7x + 6)/(x^3 - 7x^2 + 16x - 12)]`
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)]`
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 -> 3) (1/(x^2 - 11x + 24) + 1/(x^2 - x - 6))` =
Evaluate the following limits
`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)]`
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_(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_(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_(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_(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)]`
