Advertisements
Advertisements
Question
Evaluate the following limits: `lim_(x -> 0) [(sqrt(6 + x + x^2) - sqrt(6))/x]`
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_(y -> 0) [(sqrt(1 - y^2) - sqrt(1 + y^2))/y^2]`
Evaluate the following limits: `lim_(x -> "a") [(sqrt("a" + 2x) - sqrt(3x))/(sqrt(3"a" + x) - 2sqrt(x))]`
Evaluate the following limits: `lim_(x -> 1) [(x^2 + xsqrt(x) - 2)/(x - 1)]`
Evaluate the following limits: `lim_(y -> 2) [(2 - y)/(sqrt(3 - y) - 1)]`
Evaluate the following limits: `lim_(z -> 4) [(3 - sqrt(5 + z))/(1 - sqrt(5 - z))]`
Evaluate the following limit:
`lim_(x -> 0)[(sqrt(6 + x + x^2) - sqrt(6))/x]`
Evaluate the following limit :
`lim_(y -> 0)[(sqrt(1 - y^2) - sqrt(1 + y^2))/y^2]`
Evaluate the following limit :
`lim_(x -> "a") [(sqrt("a" + 2x) - sqrt(3x))/(sqrt(3"a" + x) - 2sqrt(x))]`
Evaluate the following limit :
`lim_(y -> 0) [(sqrt("a" + y) - sqrt("a"))/(ysqrt("a" + y))]`
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)[3/(xsqrt(9 - x)) - 1/x]`
Evaluate the following :
`lim_(x -> 0)[x]` ([*] is a greatest integer function.)
Evaluate the following :
If f(r) = πr2 then find `lim_("h" -> 0) [("f"("r" + "h") - "f"("r"))/"h"]`
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]`
