Advertisements
Advertisements
Question
Evaluate the following Limits: `lim_(x -> 0)[(log(4 - x) - log(4 + x))/x]`
Advertisements
Solution
`lim_(x -> 0)(log(4 - x) - log(4 + x))/x`
= `lim_(x -> 0) (log[4(1 - x/4)] - log[4(1 + x/4)])/x`
= `lim_(x -> 0)(log4 + log(1 - x/4) - [log4 log(1 + x/4)])/x`
= `lim_(x -> 0) (log(1 - x/4) - log(1 + x/4))/x`
= `lim_(x -> 0)[(log(1 - x/4))/x - (log(1 + x/4))/x]`
= `lim_(x -> 0) (log(1 - x/4))/((-4)(-x/4)) - lim_(x -> 0) (log(1 + x/4))/(4(x/4)`
= `-1/4 lim_(x -> 0) (log(1 - x/4))/(-x/4) - 1/4 lim_(x -> 0) (log(1 + x/4))/(x/4)`
= `-1/4(1) - 1/4(1) ...[("As" x -> 0"," x/4 -> 0"," (-x)/4 _> 0),(and lim_(x -> 0) (log(1 + x))/x = 1)]`
= `-1/2`
APPEARS IN
RELATED QUESTIONS
Evaluate the following: `lim_(x -> 0)[(log(2 + x) - log( 2 - x))/x]`
Evaluate the following: `lim_(x -> 0) [(3^x + 3^-x - 2)/x^2]`
Evaluate the following: `lim_(x -> 2) [(3^(x/2) - 3)/(3^x - 9)]`
Evaluate the following: `lim_(x -> 0)[((49)^x- 2(35)^x + (25)^x)/x^2]`
Evaluate the following Limits: `lim_(x -> 0)(1 + x/5)^(1/x)`
Evaluate the following Limits: `lim_(x -> 0)[(log(1 + 9x))/x]`
Evaluate the following Limits: `lim_(x -> 0)[((5^x - 1)^2)/(x*log(1 + x))]`
Evaluate the following Limits: `lim_(x -> 0) [("a"^(4x) - 1)/("b"^(2x) - 1)]`
Evaluate the following limit :
`lim_(x -> 0) [(9^x - 5^x)/(4^x - 1)]`
Evaluate the following limit :
`lim_(x -> 0)[("a"^x + "b"^x + "c"^x - 3)/sinx]`
Evaluate the following limit :
`lim_(x -> 0) [(log(3 - x) - log(3 + x))/x]`
Evaluate the following limit :
`lim_(x -> 0) [(5 + 7x)/(5 - 3x)]^(1/(3x))`
Select the correct answer from the given alternatives.
`lim_(x -> 3) [(5^(x - 3) - 4^(x - 3))/(sin(x - 3))]` =
Evaluate the following :
`lim_(x -> 0) [("a"^(3x) - "a"^(2x) - "a"^x + 1)/(x*tanx)]`
`lim_{x→∞} ((3x + 3)^40(9x - 3)^5)/(3x + 1)^45` = ______
`lim_(x -> 0) (sin^4 3x)/x^4` = ________.
The value of `lim_{x→2} (e^{3x - 6} - 1)/(sin(2 - x))` is ______
Evaluate the following:
`lim_(x->0)[((25)^x -2(5)^x+1)/x^2]`
Evaluate the following :
`lim_(x->0)[((25)^x -2 (5)^x +1)/(x^2)]`
Evaluate the following:
`lim_(x->0)[((25)^x-2(5)^x+1)/x^2]`
