Question

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. $f(x) = (x + 3x^5)^4$, $a = -1$ $\lim_{x \to -1} f(x) = \lim_{x \to -1} (\text{_____})^4$ $= \lim_{x \to -1} (\text{_____})^4$ by the power law $= (\lim_{x \to -1} (x) + \lim_{x \to -1} (\text{_____}))^4$ by the sum law $= (\lim_{x \to -1} (x) + \text{_____} \lim_{x \to -1} (x^5))^4$ by the multiple constant law $= (-1 + 3(\text{___}))^4$ by the direct substitution property $= \text{_}$ Find $f(-1)$. $f(-1) = \text{___}$ Thus, by the definition of continuity, $f$ is continuous at $a = -1$.

          Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
$f(x) = (x + 3x^5)^4$, $a = -1$
$\lim_{x \to -1} f(x) = \lim_{x \to -1} (\text{_____})^4$
$= \lim_{x \to -1} (\text{_____})^4$ by the power law
$= (\lim_{x \to -1} (x) + \lim_{x \to -1} (\text{_____}))^4$ by the sum law
$= (\lim_{x \to -1} (x) + \text{_____} \lim_{x \to -1} (x^5))^4$ by the multiple constant law
$= (-1 + 3(\text{_____}))^4$ by the direct substitution property
$= \text{_____}$
Find $f(-1)$.
$f(-1) = \text{_____}$
Thus, by the definition of continuity, $f$ is continuous at $a = -1$.

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
f(x) = (x + 3x^5)^4, a = -1
limx → -1 f(x) = limx → -1 ()^4
= limx → -1 ()^4 by the power law
= (limx → -1 (x) + limx → -1 ())^4 by the sum law
= (limx → -1 (x) + limx → -1 (x^5))^4 by the multiple constant law
= (-1 + 3())^4 by the direct substitution property
=
Find f(-1).
f(-1) =
Thus, by the definition of continuity, f is continuous at a = -1.

Added by Ashley A.

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