Advertisements
Advertisements
प्रश्न
Write the first 6 terms of the exponential series
`"e"^(-2x)`
Advertisements
उत्तर
ex = `1 + x/(∠1) + x^2/(∠2) + x^3/(∠3)`
`"e"^(-2x) = 1+ (-2x)/(∠1) + (-2x)^2/(∠2) + (-2x)^3/(∠3) - ...`
= `1 - 2x + (4x^2)/2 - (8x^2)/6 + (16x^4)/24 - (32x^5)/120 + (64x^6)/45 - ...`
= `1 - 2x + 2x^2 - (4x^3)/3 + (2x^4)/3 - (4x^5)/15 + (4x^6)/45 - ...`
APPEARS IN
संबंधित प्रश्न
Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid
`2/(3 + 4x)^2`
Find `root(3)(10001)` approximately (two decimal places
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
`"e"^(1/2x)`
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)/(1 + 2x))` Find the intervals on which the expansions are valid.
Choose the correct alternative:
The coefficient of x8y12 in the expansion of (2x + 3y)20 is
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:
If Sn denotes the sum of n terms of an AP whose common difference is d, the value of Sn − 2Sn−1 + Sn−2 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 value of `1/(2!) + 1/(4!) + 1/(6!) + ...` is
