1.3 computation of limits

1.3 COMPUTATION OF LIMITS

F t t d l bFor any constant c and any real number a,

For any real number a,

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THEOREM 3.1



EXAMPLE 3.1 Finding the Limit of a Polynomial



EXAMPLE 3.1 Finding the Limit of a Polynomial

Solution



EXAMPLE 3.3 Finding a Limit by Factoring




Solution

Notice right away thatot ce g t a ay t at

since the limit in the denominator is zero.




Solution



THEOREM 3.2



THEOREM 3.3



EXAMPLE 3.4 Evaluating the Limit of an nth Root of a P l i lPolynomial



EXAMPLE 3.4 Evaluating the Limit of an nth Root of a P l i l

Solution

Polynomial



EXAMPLE 3.5 Finding a Limit by Rationalizing

Notice that both the numerator and the denominatorNotice that both the numerator and the denominator approach 0 as x approaches 0.




Solution



THEOREM 3.4



THEOREM 3.5 (Squeeze Theorem)



EXAMPLE 3.8 Using the Squeeze Theorem to Verify the V l f Li itValue of a Limit



EXAMPLE 3.8 Using the Squeeze Theorem to Verify the V l f Li it

Solution

Value of a Limit



EXAMPLE 3.9 A Limit for a Piecewise‐Defined Function

(Consider one‐sided limits.)



EXAMPLE 3.9 A Limit for a Piecewise‐Defined Function

Solution


1.3 computation of limits

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