Advertisements
Advertisements
Question
Evaluate the Following limit :
`lim_(z -> 4) [(3 - sqrt(5 + z))/(1 - sqrt(5 - z))]`
Solution
`lim_(z -> 4) (3 - sqrt(5 + z))/(1 - sqrt(5 - z))`
= `lim_(z -> 4) (3 - sqrt(5 + z))/(1 - sqrt(5 - z)) xx (3 + sqrt(5 + z))/(3 + sqrt(5 + z)) xx (1 + sqrt(5 - z))/(1 + sqrt(5 - z))`
= `lim_(z -> 4) ([9 - (5 + z)][1 + sqrt(5 - z)])/([1 - (5 - z)][3 + sqrt(5 + z)])`
= `lim_(z -> 4) (-(z - 4)[1 + sqrt(5 - z)])/((z - 4)[3 + sqrt(5 + z)])`
= `lim_(z -> 4) (-[1 + sqrt(5 - z)])/([3 + sqrt(5 + z)]) ...[(because z -> 4"," z ≠ 4),(therefore z - 4 ≠ 0)]`
= `(-lim_(z -> 4) [1 + sqrt(5 - z)])/(lim_(z -> 4) [3 + sqrt(5 + z)])`
= `(-[1 + sqrt(5 - 4)])/([3 + sqrt(5 + 4)])`
= `(-[1 + 1])/(3 + 3)`
= `-1/3.`
APPEARS IN
RELATED QUESTIONS
Evaluate the following limits: `lim_(x -> 0) [(sqrt(6 + x + x^2) - sqrt(6))/x]`
Evaluate the following limits: `lim_(x -> 2)[(sqrt(2 + x) - sqrt(6 - x))/(sqrt(x) - sqrt(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 -> 0)[(sqrt(1 + x^2) - sqrt(1 + x))/(sqrt(1 + x^3) - sqrt(1 + x))]`
``Evaluate the following limits: `lim_(x -> 4) [(x^2 + x - 20)/(sqrt(3x + 4) - 4)]`
Evaluate the following limits: `lim_(x -> 2) [(x^3 - 8)/(sqrt(x + 2) - sqrt(3x - 2))]`
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_(x -> 3)[(sqrt(2x + 3) - sqrt(4x - 3))/(x^2 - 9)]`
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_(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_(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]`
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]`
