English

Evaluate the following Limits: limx→0(1+x5)1x

Advertisements
Advertisements

Question

Evaluate the following Limits: `lim_(x -> 0)(1 + x/5)^(1/x)`

Sum
Advertisements

Solution

`lim_(x -> 0)(1 + x/5)^(1/x)`

= `lim_(x -> 0)[(1 + x/5)^(5/x)]^(1/5)`

= `"e"^(1/5)       ...[lim_(x -> 0) (1 + x)^(1/x) = "e"]`

shaalaa.com
  Is there an error in this question or solution?
Chapter 7: Limits - MISCELLANEOUS EXERCISE - 7 [Page 106]

APPEARS IN

RELATED QUESTIONS

Evaluate the following: `lim_(x -> 0)[(9^x - 5^x)/(4^x - 1)]`


Evaluate the following: `lim_(x -> 0) [(3^x + 3^-x - 2)/x^2]`


Evaluate the following: `lim_(x -> 0) [(2^x - 1)^2/((3^x - 1) xx log (1 + x))]`


Evaluate the following Limits: `lim_(x -> 0)[(x(6^x - 3^x))/((2^x - 1)*log(1 + x))]`


Evaluate the following Limits: `lim_(x -> 0)[(log 100 + log (0.01 + x))/x]`


Evaluate the following limit : 

`lim_(x -> 0) [(9^x - 5^x)/(4^x - 1)]`


Evaluate the following limit : 

`lim_(x -> 0) [(3^x + 3^-x - 2)/(x*tanx)]`


Evaluate the following limit : 

`lim_(x -> 0)[(4x + 1)/(1 - 4x)]^(1/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) ((15^x - 3^x - 5^x + 1)/sin^2x)` =


Select the correct answer from the given alternatives.

`lim_(x -> 0) [(x*log(1 + 3x))/("e"^(3x) - 1)^2]` =


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 -> 2) [(logx - log2)/(x - 2)]`


`lim_{x→∞} ((3x + 3)^40(9x - 3)^5)/(3x + 1)^45` = ______ 


The value of `lim_{x→-∞} (sqrt(5x^2 + 4x + 7))/(5x + 4)` is ______ 


If f: R → R is defined by f(x) = [x - 2] + |x - 5| for x ∈ R, then `lim_{x→2^-} f(x)` is equal to ______ 


lf the function f(x) satisfies `lim_{x→1}(2f(x) - 5)/(2(x^2 - 1)) = e`, then `lim_{x→1}f(x)` is ______ 


Evaluate the following:

`lim_(x->0)[((25)^x -2(5)^x +1)/(x^2)]`


\[\lim_{x\to0}\frac{\mathrm{e}^{\tan x}-\mathrm{e}^{x}}{\tan x-x}=\]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×