Advertisements
Advertisements
Question
Write the first 4 terms of the logarithmic series
log(1 + 4x) Find the intervals on which the expansions are valid.
Solution
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
RELATED QUESTIONS
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`
Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid
`(5 + x^2)^(2/3)`
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 `root(3)(x^3 + 6) - root(3)(x^3 + 3)` is approximately equal to `1/x^2` when x is sufficiently large
Write the first 6 terms of the exponential series
e5x
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) + ...`
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 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:
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 value of `1 - 1/2(2/3) + 1/3(2/3)^2 1/4(2/3)^3 + ...` is
