# What will be the expansion of #sqrt(x+h)# in powers of #x and h#?

Since it is very hard to find power expansions for any case, we are unable to expand this in a general case; however, we can estimate it in the limit of one being much larger than the other, and then discuss that case.

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The expansion of sqrt(x+h) in powers of x and h is given by:

sqrt(x+h) = sqrt(x) + (1/2)*(h/x)*sqrt(x) - (1/8)*(h^2/x^2)*sqrt(x) + (1/16)*(h^3/x^3)*sqrt(x) - (5/128)*(h^4/x^4)*sqrt(x) + ...

This expansion can be continued indefinitely, with each term involving higher powers of h and lower powers of x.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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