In order to take limits in Mathcad let’s introduce a few concepts which will be in use later. Number **m** is the limit of the number sequence** {ai}**,if for every positive number there is a dependent on it natural number, **N**, and for all given **n > N** exists inequality ** | an –m | <** . It is written down the following way:

Number **m** is the limit of function f(x) in finite or infinite point **f(x)** in finite or infinite point ** х0**, if for every number sequence **хn, n = 1,2,…,** converging to **х0**, sequence **f(xn)** , **n = 1,2,… **converges to **m**. In this case, it is written down the following way:

. If , we observe the right-hand limit of function **y = f(x)**. If , we observe the left-hand limit of the function.

The same symbols are in use in Mathсad. At the same time the following table of symbols is in use for calculating the limits of number sequence and function, the right-hand and the left-hand limits of function:

While calculating limits in Mathcad only the symbol of the symbolic equality is in use. While calculations are carried out, besides results various messages can come out. It the expression is entered the wrong way, Mathcad shows the notification: “ **No symbolic result was found**”. If Mathсad cannot compute the expression, the given problem is repeated instead of its solution. If the limit does not exist, the result of calculations will come out as: “**Undefined**”. The example is shown in the programme listing.

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