Advertisements
Advertisements
प्रश्न
Select the correct answer from the given alternatives.
`lim_(x→0)[(3^(sinx) - 1)^3/((3^x - 1).tan x.log(1 + x))]` =
पर्याय
3log 3
2log 3
(log 3)2
(log 3)3
Advertisements
उत्तर
`lim_(x→0)[(3^(sinx) − 1)^3/((3^x − 1).tan x.log(1 + x))]` = (log 3)2
Explanation:
`lim_(x→0)[(3^(sinx) - 1)^3/((3^x - 1).tan x.log(1 + x))]`
`= (lim_(x →0) (3^(sin x) - 1)^3/(sin^3 x). (sin^3 x)/(x^3))/(lim_(x →0) ((3^x − 1)/x).(tan x/x).log(1 + x)/x)`
`= (lim_(x →0) ((3^(sinx) - 1)/sin x)^3. lim_(x →0) (sin x/x)^3)/(lim_(x →0) ((3^x − 1)/x). lim_(x →0) (tan x/x). lim_(x →0) (log(1 + x)/x))`
`= ((log 3)^3 × (1)^3)/(log 3 × 1 × 1)`
`= (log 3)^3/(log 3)`
= (log 3)2
APPEARS IN
संबंधित प्रश्न
Evaluate the following: `lim_(x -> 0)[(9^x - 5^x)/(4^x - 1)]`
Evaluate the following: `lim_(x -> 0)[(log(2 + x) - log( 2 - x))/x]`
Evaluate the following: `lim_(x -> 0) [(3 + x)/(3 - x)]^(1/x)`
Evaluate the following: `lim_(x -> 0)[(log(3 - x) - log(3 + x))/x]`
Evaluate the following: `lim_(x -> 0) [(2^x - 1)^2/((3^x - 1) xx log (1 + x))]`
Evaluate the following:
`lim_(x ->0)[((25)^x - 2(5)^x + 1)/x^2]`
Evaluate the following Limits: `lim_(x -> 0)[(5^x - 1)/x]`
Evaluate the following Limits: `lim_(x -> 0)[("a"^x + "b"^x + "c"^x - 3)/x]`
Evaluate the following Limits: `lim_(x -> 0) ("e"^x + e^(-x) - 2)/x^2`
Evaluate the following Limits: `lim_(x -> 0) [("a"^(4x) - 1)/("b"^(2x) - 1)]`
Evaluate the following Limits: `lim_(x -> 0)[(log 100 + log (0.01 + x))/x]`
Evaluate the following Limits: `lim_(x -> 0)[(log(4 - x) - log(4 + x))/x]`
Evaluate the following limit :
`lim_(x -> 0) [(6^x + 5^x + 4^x - 3^(x + 1))/sinx]`
Evaluate the following limit :
`lim_(x -> 0) [(log(3 - x) - log(3 + x))/x]`
Evaluate the following limit :
`lim_(x -> 0)[(4x + 1)/(1 - 4x)]^(1/x)`
Evaluate the following limit :
`lim_(x -> 0) [(5 + 7x)/(5 - 3x)]^(1/(3x))`
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)]`
Evaluate the following limit :
`lim_(x -> 0) [((49)^x - 2(35)^x + (25)^x)/(sinx* log(1 + 2x))]`
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 -> 0) [(x*log(1 + 3x))/("e"^(3x) - 1)^2]` =
`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)]`
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)]`
\[\lim_{x\to0}\frac{\mathrm{e}^{\tan x}-\mathrm{e}^{x}}{\tan x-x}=\]
