मराठी

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

Advertisements
Advertisements

प्रश्न

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

बेरीज
Advertisements

उत्तर

`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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Limits - MISCELLANEOUS EXERCISE - 7 [पृष्ठ १०६]

APPEARS IN

बालभारती Mathematics and Statistics (Commerce) Part 1 [English] Standard 11 Maharashtra State Board
पाठ 7 Limits
MISCELLANEOUS EXERCISE - 7 | Q II. 8) | पृष्ठ १०६

संबंधित प्रश्‍न

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


Evaluate the following: `lim_(x -> 0)[(15^x - 5^x - 3^x +1)/x^2]`


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)[(x(6^x - 3^x))/((2^x - 1)*log(1 + x))]`


Evaluate the following limit : 

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


Evaluate the following limit : 

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


Evaluate the following limit : 

`lim_(x ->0) [("a"^x - "b"^x)/(sin(4x) - sin(2x))]`


Evaluate the following limit : 

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


Evaluate the following limit : 

`lim_(x -> 0)[(15^x - 5^x - 3^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]` =


Evaluate the following :

`lim_(x -> 0) [("a"^(3x) - "a"^(2x) - "a"^x + 1)/(x*tanx)]`


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]`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×