Advertisements
Advertisements
प्रश्न
Prove that `sqrt((1 - x)/(1 + x))` is approximately euqal to `1 - x + x^2/2` when x is very small
Advertisements
उत्तर
L.H.S = `sqrt((1 - x)/(1 + x))`
= `(1 - x)^(1/2)/(1 + x)^((-1)/2)`
= `(1 - x)^(1/2) (1 + x)^((-1)/2)`
= `(1 - 1/2 x + (1/2(- 1/2))/(2*1) x^2 ....)(1 - 1/2 x + ((1/2)(3/2))/(2*1) x^2 ....)`
= `(1 - x/2 - x^2/8 ...)(1 - x/2 + (3x^2)/8 ...)`
=`1 - x/2 + (3x^2)/8 - x/2 + x^2/4 - x^2/8 ...`
= `(1 - 2x)/2 + (4x^2)/8 + ....`
= `1 - x + x^2/2`
= R.H.S
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`
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`
Write the first 6 terms of the exponential series
e5x
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) Find the intervals on which the expansions are valid.
Find the value of `sum_("n" = 1)^oo 1/(2"n" - 1) (1/(9^("n" - 1)) + 1/(9^(2"n"- 1)))`
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 a is the arithmetic mean and g is the geometric mean of two numbers, then
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 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
Choose the correct alternative:
The value of `1 - 1/2(2/3) + 1/3(2/3)^2 1/4(2/3)^3 + ...` is
