Advertisements
Advertisements
प्रश्न
Evaluate the following limit :
`lim_(x -> 0)[(4x + 1)/(1 - 4x)]^(1/x)`
Advertisements
उत्तर
`lim_(x -> 0)[(4x + 1)/(1 - 4x)]^(1/x)`
= `lim_(x -> 0) [(1 + 4x)/(1 - 4x)]^(1/x)`
= `lim_(x -> 0) (1 + 4x)^(1/x)/(1 - 4x)^(1/x)`
= `(lim_(x -> 0) (1 + 4x)^(1/x))/(lim_(x -> 0) (1 - 4x)^(1/x))`
= `(lim_(x -> 0) [(1 + 4x)^(1/(4x))]^4)/(lim_(x -> 0)[(1 - 4x)^(-1/(4x))]^-4`
= `([lim_(x -> 0) (1 + 4x)^(1/(4x))]^4)/([lim_(x -> 0) (1 - 4x)^(-1/(4x))]^-4`
= `"e"^4/"e"^(-4) ...[because x -> 0"," ± 4x -> 0 and lim_(x -> 0) (1 + x)^x = "e"]`
= e8.
APPEARS IN
संबंधित प्रश्न
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) [("a"^(3x) - "b"^(2x))/(log 1 + 4x)]`
Evaluate the following: `lim_(x -> 0)[((49)^x- 2(35)^x + (25)^x)/x^2]`
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)[((5^x - 1)^2)/(x*log(1 + x))]`
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) [(8^sinx - 2^tanx)/("e"^(2x) - 1)]`
Evaluate the following limit :
`lim_(x -> 0) [(3^x + 3^-x - 2)/(x*tanx)]`
Evaluate the following limit :
`lim_(x -> 0) [(3 + x)/(3 - x)]^(1/x)`
Evaluate the following limit :
`lim_(x -> 0)[(5x + 3)/(3 - 2x)]^(2/x)`
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) [(x*log(1 + 3x))/("e"^(3x) - 1)^2]` =
Evaluate the following :
`lim_(x -> 0) [("a"^(3x) - "a"^(2x) - "a"^x + 1)/(x*tanx)]`
Evaluate the following :
`lim_(x -> 2) [(logx - log2)/(x - 2)]`
Evaluate the following :
`lim_(x -> 0) [((5^x - 1)^2)/((2^x - 1)log(1 + x))]`
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) (log(1 + (5x)/2))/x` is equal to ______.
The value of `lim_{x→0} (1 + sinx - cosx + log_e(1 - x))/x^3` is ______
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 limit :
`lim(x>2)[(z^2 -5z+6)/(z^2-4)]`
Evaluate the following limit :
`lim_(x->0)[(sqrt(6+x+x^2)-sqrt6)/x]`
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 limit:
`lim_(z->2)[(z^2-5x+6)/(z^2-4)]`
Evaluate the following:
`lim_(x->0)[((25)^x -2(5)^x +1)/(x^2)]`
\[\lim_{x\to0}\frac{\mathrm{e}^{\tan x}-\mathrm{e}^{x}}{\tan x-x}=\]
