Advertisements
Advertisements
प्रश्न
Write the first 6 terms of the exponential series
e5x
Advertisements
उत्तर
ex = `1 + x/(∠1) + x^2/(∠2) + x^3/(∠3)`
So e5x = `1 (5x)/(∠1) + (5x)^2/(∠2) + (5x)^3/(∠3) + (5x)^4/(∠4) + ....`
= `1 + 5x + (25x^2)/2 + (125x^3)/6 + (625x^4)/24 + 3125/120 x^5 + 15625/72 x^6 ...`
= `1 + 5x + (25x^2)/2 + (125x^3)/6 + (625x^4)/24 + (625x^5)/24 + (3125x^6)/144 ...`
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"^(-2x)`
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 + 3x)/(1 -3x))` Find the intervals on which the expansions are valid.
If p − q is small compared to either p or q, then show `root("n")("p"/"q")` ∼ `(("n" + 1)"p" + ("n" - 1)"q")/(("n"- 1)"p" +("n" + 1)"q")`. Hence find `root(8)(15/16)`
Choose the correct alternative:
The coefficient of x6 in (2 + 2x)10 is
Choose the correct alternative:
If a is the arithmetic mean and g is the geometric mean of two numbers, then
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 sum of an infinite GP is 18. If the first term is 6, the common ratio is
