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Prove that root(3)(x^(3)+6)-root(3)(x^(3...

Prove that `root(3)(x^(3)+6)-root(3)(x^(3)+3)` is approximately equal to `1/x^(2)` when x is sufficiently large.

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SURA PUBLICATION-BINOMIAL THEOREM, SEQUENCES AND SERIES-EXERCISE 5.4
  1. Expand the following in ascending powers of x and find the condition o...

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  2. Expand the following in ascending powers of x and find the condition o...

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  3. Expand the following in ascending powers of x and find the condition o...

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  4. Expand the following in ascending powers of x and find the condition o...

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  5. Find root(3)(1001) approximately. (two decimal places).

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  6. Prove that root(3)(x^(3)+6)-root(3)(x^(3)+3) is approximately equal to...

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  7. Prove that sqrt((1-x)/(1+x)) is approximately equal to 1-x+x^(2)/2 whe...

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  8. Write the first 6 terms of the exponential series e^(5x)

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  9. Write the first 6 terms of the exponential series e^(-2x)

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  10. Write the first 6 terms of the exponential series e^(1/2x)

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  11. Write the first 4 terms of the logarithmic series log(1+4x) Find t...

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  12. Write the first 4 terms of the logarithmic series log(1-2x) Find t...

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  13. Write the first 4 terms of the logarithmic series log((1+3x)/(1-3x))...

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  14. Write the first 4 terms of the logarithmic series log((1-2x)/(1+2x))...

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  15. If y=x+x^(2)/2+x^(3)/3+x^(4)/4+... then show that x=y-y^(2)/(2!)+y^(3)...

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  16. If p - q is small compared to either p or q, then show that sqrt(p/q)=...

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  17. Find the co-efficient of x^(4) in the expansion of (3-4x+x^(2))/e^(2x)...

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