Advertisements
Advertisements
प्रश्न
Evaluate the following Limits: `lim_(x -> 0)[(log(4 - x) - log(4 + x))/x]`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Evaluate the following: `lim_(x -> 0)[(9^x - 5^x)/(4^x - 1)]`
Evaluate the following Limits: `lim_(x -> 0)[("a"^x + "b"^x + "c"^x - 3)/x]`
Evaluate the following Limits: `lim_(x -> 0)[(log 100 + log (0.01 + x))/x]`
Evaluate the following limit :
`lim_(x -> 0) [(5^x + 3^x - 2^x - 1)/x]`
Evaluate the following limit :
`lim_(x -> 0) [(3^x + 3^-x - 2)/(x*tanx)]`
Evaluate the following limit :
`lim_(x -> 0)[(5x + 3)/(3 - 2x)]^(2/x)`
Evaluate the following limit :
`lim_(x -> 0) [((25)^x - 2(5)^x + 1)/(x*sinx)]`
Select the correct answer from the given alternatives.
`lim_(x -> 0) [(log(5 + x) - log(5 - x))/sinx]` =
Select the correct answer from the given alternatives.
`lim_(x -> pi/2) ((3^(cosx) - 1)/(pi/2 - x))` =
Select the correct answer from the given alternatives.
`lim_(x→0)[(3^(sinx) - 1)^3/((3^x - 1).tan x.log(1 + x))]` =
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 -> 1) [("ab"^x - "a"^x"b")/(x^2 - 1)]`
The value of `lim_{x→-∞} (sqrt(5x^2 + 4x + 7))/(5x + 4)` is ______
lf the function f(x) satisfies `lim_{x→1}(2f(x) - 5)/(2(x^2 - 1)) = e`, then `lim_{x→1}f(x)` is ______
`lim_(x -> 0) (15^x - 3^x - 5^x + 1)/(xtanx)` is equal to ______.
Evaluate the following:
`lim_(x->0)[((25)^x -2(5)^x+1)/x^2]`
Evaluate the following Limit.
`lim_(x->1)[(x^3-1)/(x^2+5x-6)]`
Evaluate the following:
`lim_(x->0) [((25)^x - 2(5)^x + 1)/x^2]`
