Advertisements
Advertisements
प्रश्न
Evaluate the following limit :
`lim_(x -> sqrt(2)) [(x^2 + xsqrt(2) - 4)/(x^2 - 3xsqrt(2) + 4)]`
Advertisements
उत्तर
`lim_(x -> sqrt(2)) [(x^2 + xsqrt(2) - 4)/(x^2 - 3xsqrt(2) + 4)]`
Consider, `x^2 + xsqrt(2) - 4 = x^2 + sqrt(2) x - 4`
= `x^2 + 2sqrt(2)x - sqrt(2)x - 4`
= `x(x + 2sqrt(2)) - sqrt(2)(x + 2sqrt(2))`
= `(x + 2sqrt(2)) (x - sqrt(2))`
`x^2 - 3x sqrt(2) + 4 = x^2 - 3sqrt(2)x + 4`
= `x^2 - 2sqrt(2)x - sqrt(2)x + 4`
= `x(x - 2sqrt(2)) - sqrt(2)(x - 2sqrt(2))`
= `(x - 2sqrt(2)) (x - sqrt(2))`
Now, `lim_(x -> sqrt(2)) [(x^2 + xsqrt(2) - 4)/(x^2 - 3xsqrt(2) + 4)]`
= `lim_(x -> sqrt(2)) ((x + 2sqrt(2))(x - sqrt(2)))/((x - 2sqrt(2))(x - sqrt(2))`
= `lim_(x -> sqrt(2)) (x + 2sqrt(2))/(x - 2sqrt(2)) ...[(because x -> sqrt(2)"," therefore x ≠ sqrt(2)","),(therefore x - sqrt(2)≠ 0)]`
= `(lim_(x -> sqrt(2))(x + 2sqrt(2)))/(lim_(x -> sqrt(2))(x - 2sqrt(2))`
= `(sqrt(2) + 2sqrt(2))/(sqrt(2) - 2sqrt(2))`
= `(3sqrt(2))/(-sqrt(2))`
= – 3
APPEARS IN
संबंधित प्रश्न
Evaluate the following limits: `lim_(x -> 3)[(x^2 + 2x - 15)/(x^2 - 5x + 6)]`
Evaluate the following Limits: `lim_(x -> 2)[((x - 2))/(2x^2 - 7x + 6)]`
Evaluate the following limit:
`lim_(z -> 2) [(z^2 - 5z + 6)/(z^2 - 4)]`
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 -> 2)[(x^3 - 4x^2 + 4x)/(x^2 - 1)]`
Evaluate the following limit :
`lim_(x -> 2) [(x^3 - 7x + 6)/(x^3 - 7x^2 + 16x - 12)]`
Evaluate the following limit :
`lim_(x -> 1) [(x - 2)/(x^2 - x) - 1/(x^3 - 3x^2 + 2x)]`
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 -> -2)((x^7 + 128)/(x^3 + 8))` =
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->-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)]`
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 -> 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 limits:
`lim_(z→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-> -2)[(x^7 + x^5 + 160)/(x^3 +8)]`
