Advertisements
Advertisements
प्रश्न
Write the first 4 terms of the logarithmic series
log(1 + 4x) Find the intervals on which the expansions are valid.
Advertisements
उत्तर
lo(1 + x) = `x - x^2/2 + x^3/3 - x^4/4 ...`
log(1 – x) = `x - x^2/2 - x^3/3 ...`
log(1 + 4x) = `4x - (4x)^2/2 + (4x)^3/3 - (4x)^4/4 ...`
Hence |4x| < 1
⇒ |x| < `1/4`
= `4x - (16x^2)/2 + (64x^3)/3 - (256x^4)/4 ...`
= `4x - 8x^2 + 64/3 x^3 - 64x^4 ...`
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
`1/(5 + x)`
Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid
`(x + 2) - 2/3`
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 4 terms of the logarithmic series
log(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) + ...`
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)`
Find the coefficient of x4 in the expansion `(3 - 4x + x^2)/"e"^(2x)`
Choose the correct alternative:
The coefficient of x6 in (2 + 2x)10 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
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
