1.3 COMPUTATION OF LIMITS
Transcript of 1.3 COMPUTATION OF LIMITS
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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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1.3 COMPUTATION OF LIMITS
THEOREM 3.1
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.1 Finding the Limit of a Polynomial
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.1 Finding the Limit of a Polynomial
Solution
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.3 Finding a Limit by Factoring
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1.3 COMPUTATION OF LIMITS
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.
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.3 Finding a Limit by Factoring
Solution
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1.3 COMPUTATION OF LIMITS
THEOREM 3.2
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1.3 COMPUTATION OF LIMITS
THEOREM 3.3
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.4 Evaluating the Limit of an nth Root of a P l i lPolynomial
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.4 Evaluating the Limit of an nth Root of a P l i l
Solution
Polynomial
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1.3 COMPUTATION OF LIMITS
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.
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.5 Finding a Limit by Rationalizing
Solution
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.5 Finding a Limit by Rationalizing
Solution
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1.3 COMPUTATION OF LIMITS
THEOREM 3.4
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1.3 COMPUTATION OF LIMITS
THEOREM 3.4
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1.3 COMPUTATION OF LIMITS
THEOREM 3.5 (Squeeze Theorem)
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.8 Using the Squeeze Theorem to Verify the V l f Li itValue of a Limit
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.8 Using the Squeeze Theorem to Verify the V l f Li it
Solution
Value of a Limit
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.8 Using the Squeeze Theorem to Verify the V l f Li it
Solution
Value of a Limit
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.9 A Limit for a Piecewise‐Defined Function
(Consider one‐sided limits.)
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1.3 COMPUTATION OF LIMITS
EXAMPLE 3.9 A Limit for a Piecewise‐Defined Function
Solution
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