Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises: 38

Answer

$9$

Work Step by Step

$\lim\limits_{x \to 4} 3^{\sqrt {x^{2} -2x-4}} =$ $\lim\limits_{x \to 4} 3^{\sqrt {4^{2} -2(4)-4}} =$ $3^{\sqrt {16 -8-4}} =$ $3^{\sqrt {16 -12}} =$ $3^{\sqrt {4}} =$ $ 3^{2} = 9$ (We see that the function is a composite of an exponential function, square root function, and a polynomial function. We can see that $4$ is in the domain of the function and that the function is continuous at $4$. Thus the limit can be evaluated at $4$ by plugging in $x=4$.)
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