Advertisements
Advertisements
Question
Evaluate the following limits: `lim_(x -> 0) [(sqrt(6 + x + x^2) - sqrt(6))/x]`
Advertisements
Solution
`lim_(x -> 0) [(sqrt(6 + x + x^2) - sqrt(6))/x]`
= `lim_(x -> 0) [(sqrt(6 + x + x^2) - sqrt(6))/x xx (sqrt(6 + x + x^2) + sqrt(6))/(sqrt(6 + x + x^2) + sqrt(6))]`
= `lim_(x -> 0) ((6 + x + x^2) - 6)/(x(sqrt(6 + x + x^2) + sqrt(6))`
= `lim_(x -> 0)(x + x^2)/(x(sqrt(6 + x + x^2) + sqrt(6))`
= `lim_(x -> 0) (x (1 + x))/(x(sqrt(6 + x + x^2) + sqrt(6))`
= `lim_(x -> 0) (1 + x)/(sqrt(6 + x + x^2) + sqrt(6)` ...[∵ x → 0, ∴ x ≠ 0]
= `((1 + 0))/(sqrt(6) + sqrt(6)`
= `1/(2sqrt(6))`
APPEARS IN
RELATED QUESTIONS
Evaluate the following limits: `lim_(x -> 2)[(sqrt(2 + x) - sqrt(6 - x))/(sqrt(x) - sqrt(2))]`
Evaluate the following limits: `lim_(x -> 0)[(sqrt(1 + x^2) - sqrt(1 + x))/(sqrt(1 + x^3) - sqrt(1 + x))]`
Evaluate the following limits: `lim_(y -> 2) [(2 - y)/(sqrt(3 - y) - 1)]`
Evaluate the following limit:
`lim_(x -> 0)[(sqrt(6 + x + x^2) - sqrt(6))/x]`
Evaluate the following limit :
`lim_(x -> 3)[(sqrt(2x + 3) - sqrt(4x - 3))/(x^2 - 9)]`
Evaluate the following limit :
`lim_(x -> "a") [(sqrt("a" + 2x) - sqrt(3x))/(sqrt(3"a" + x) - 2sqrt(x))]`
Evaluate the following limit :
`lim_(x -> 2)[(sqrt(1 + sqrt(2 + x)) - sqrt(3))/(x - 2)]`
Evaluate the following limit :
`lim_(x -> 0)[(sqrt(x^2 + 9) - sqrt(2x^2 + 9))/(sqrt(3x^2 + 4) - sqrt(2x^2 + 4))]`
Evaluate the following limit :
`lim_(x -> 1) [(x^2 + xsqrt(x) - 2)/(x - 1)]`
Evaluate the Following limit :
`lim_(x -> 4) [(x^2 + x - 20)/(sqrt(3x + 4) - 4)]`
Evaluate the Following limit :
`lim_(z -> 4) [(3 - sqrt(5 + z))/(1 - sqrt(5 - z))]`
Evaluate the following limit:
`lim_(x->0)[(sqrt(6 + x + x^2) - sqrt6)/x]`
Evaluate the following limit:
`lim_(x->0)[(sqrt(6+x+x^2)-sqrt6)/x]`
Evaluate the following limit:
`lim_(x->0)[(sqrt(6+x+x^2)-sqrt6)/x]`
Evaluate the following limit.
`lim_(x→0) [[sqrt(6 + x + x^2)- sqrt6]/x]`
Evaluate the following limit:
`lim_(x->0)[(sqrt(6 + x + x^2) - sqrt6)/ (x)]`
\[\lim_{x\to3}\frac{(84-x)^{\frac{1}{4}}-3}{x-3}\mathrm{~is}\]
