मराठी
तामिळनाडू बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान इयत्ता ११

Write the first 6 terms of the exponential seriesee12x

Advertisements
Advertisements

प्रश्न

Write the first 6 terms of the exponential series
`"e"^(1/2x)`

बेरीज
Advertisements

उत्तर

ex = `1 + x/(∠1) + x^2/(∠2) + x^3/(∠3)`

`"e"^(1/2x) = 1+ 1/2x + (1/2 x)^2/(∠2) + (1/2 x)^3/(∠3) ...`

= `1+ x/2 + x^2/8 + x^3/48 + x^4/384 + x^5/3840 + ...`

shaalaa.com
Infinite Sequences and Series
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Binomial Theorem, Sequences and Series - Exercise 5.4 [पृष्ठ २३१]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 5 Binomial Theorem, Sequences and Series
Exercise 5.4 | Q 5. (iii) | पृष्ठ २३१

संबंधित प्रश्‍न

Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid

`1/(5 + x)`


Find `root(3)(10001)` approximately (two decimal places


Prove that `root(3)(x^3 + 6) - root(3)(x^3 + 3)` is approximately equal to `1/x^2` when x is sufficiently large


Prove that `sqrt((1 - x)/(1 + x))` is approximately euqal to `1 - x + x^2/2` when x is very small


Write the first 6 terms of the exponential series
e5x 


Write the first 4 terms of the logarithmic series
log(1 + 4x) Find the intervals on which the expansions are valid.


Write the first 4 terms of the logarithmic series
log(1 – 2x) Find the intervals on which the expansions are valid.


Write the first 4 terms of the logarithmic series
`log((1 - 2x)/(1 + 2x))` Find the intervals on which the expansions are valid.


If y = `x + x^2/2 + x^3/3 + x^4/4  ...`, then show that x = `y - y^2/(2!) + y^3/(3!) - y^4/(4) + ...`


Find the coefficient of x4 in the expansion `(3 - 4x + x^2)/"e"^(2x)`


Choose the correct alternative:
If (1 + x2)2 (1 + x)n = a0 + a1x + a2x2 + …. + xn + 4 and if a0, a1, a2 are in AP, then n is


Choose the correct alternative:
The sum up to n terms of the series `1/(sqrt(1)  +sqrt(3)) + 1/(sqrt(3) + sqrt(5)) + 1/(sqrt(5) + sqrt(7)) + ...` is 


Choose the correct alternative:
The value of the series `1/2 + 7/4 + 13/8 + 19/16 + ...` is


Choose the correct alternative:
The sum of an infinite GP is 18. If the first term is 6, the common ratio is


Choose the correct alternative:
The coefficient of x5 in the series e-2x is


Choose the correct alternative:
The value of `1/(2!) + 1/(4!) + 1/(6!) + ...` is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×