Advertisements
Advertisements
प्रश्न
Evaluate the following: `lim_(x -> 0)[(log(3 - x) - log(3 + x))/x]`
Advertisements
उत्तर
`lim_(x -> 0)(log(3 - x) - log(3 + x))/x`
= `lim_(x -> 0) 1/x log ((3 - x)/(3 + x))`
= `lim_(x -> 0) log((3 - x)/(3 + x))^(1/x)`
= `lim_(x -> 0) log((1 - x/3)/(1 + x/3))^(1/x)`
= `log[lim_(x -> 0) ((1 - x/3)^(1/x))/(1 + x/3)^(1/x)]`
= `log[({lim_(x -> 0)(1 - x/3)^((-3)/x)}^((-1)/3))/({lim_(x -> 0)(1 + x/3)^(3/x)}^(1/3))]`
= `log(("e"^(-1/3))/("e"^(1/3))) ...[because x -> 0"," ± x/3 ->0 and lim_(x->0)(1 + x)^(1/x) ="e"]`
= `log "e"^((-2)/3)`
= `-2/3*log "e"`
= `-2/3(1)`
= `-2/3`
APPEARS IN
संबंधित प्रश्न
Evaluate the following: `lim_(x -> 0)[((49)^x- 2(35)^x + (25)^x)/x^2]`
Evaluate the following Limits: `lim_(x -> 0)[(5^x - 1)/x]`
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 limit :
`lim_(x -> 0) [(9^x - 5^x)/(4^x - 1)]`
Evaluate the following limit :
`lim_(x -> 0)[(15^x - 5^x - 3^x + 1)/(x*sinx)]`
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) ((15^x - 3^x - 5^x + 1)/sin^2x)` =
Select the correct answer from the given alternatives.
`lim_(x→0)[(3^(sinx) - 1)^3/((3^x - 1).tan x.log(1 + x))]` =
Evaluate the following :
`lim_(x -> 2) [(logx - log2)/(x - 2)]`
Evaluate the following :
`lim_(x -> 1) [("ab"^x - "a"^x"b")/(x^2 - 1)]`
The value of `lim_{x→0}{(a^x + b^x + c^x + d^x)/4}^{1/x}` is ______
If the function
f(x) = `(("e"^"kx" - 1)tan "kx")/"4x"^2, x ne 0`
= 16 , x = 0
is continuous at x = 0, then k = ?
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]`
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)]`
Evaluate the following:
`lim_(x -> 0)[((25)^x - 2(5)^x + 1)/x^2]`
