suppose $g(x) = f(7 - x)$ for all $x$, $\lim_{x \to 7^+} f(x) = 6$, and $\lim_{x \to 7^-} f(x) = 8$. find $\lim_{x \to 0^+} g(x)$ and $\lim_{x \to 0^-} g(x)$.

$\lim_{x \to 0^+} g(x) = 8$ (type an integer or a decimal.)
$\lim_{x \to 0^-} g(x) = \square$ (type an integer or a decimal.)

Question

suppose $g(x) = f(7 - x)$ for all $x$, $\lim_{x \to 7^+} f(x) = 6$, and $\lim_{x \to 7^-} f(x) = 8$. find $\lim_{x \to 0^+} g(x)$ and $\lim_{x \to 0^-} g(x)$.

$\lim_{x \to 0^+} g(x) = 8$ (type an integer or a decimal.)
$\lim_{x \to 0^-} g(x) = \square$ (type an integer or a decimal.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "One-Sided Limits", "Limit Substitution" ], "new_concepts": [ "Limit Composition", "Variable Substitution in Limits" ], "current_concepts": [ "One-Sided Limits", "Limit Substitution", "Limit Composition" ] } ## Analyze the limit of g(x) as x approaches 0 from the right $$ \begin{aligned} &u = 7 - x \ &x \to 0^+ \implies u \to 7^- \ &\lim_{x \to 0^+} g(x) = \lim_{x \to 0^+} f(7 - x) = \lim_{u \to 7^-} f(u) = 8 \end{aligned} $$ ## Analyze the limit of g(x) as x approaches 0 from the left $$ \begin{aligned} &u = 7 - x \ &x \to 0^- \implies u \to 7^+ \ &\lim_{x \to 0^-} g(x) = \lim_{x \to 0^-} f(7 - x) = \lim_{u \to 7^+} f(u) = 6 \end{aligned} $$ Suppose $g(x) = f(7 - x)$ for all $x$, $\lim_{x \to 7^+} f(x) = 6$, and $\lim_{x \to 7^-} f(x) = 8$. Find $\lim_{x \to 0^+} g(x)$ and $\lim_{x \to 0^-} g(x)$. $\lim_{x \to 0^+} g(x) =$ 8 (Type an integer or a decimal.) $\lim_{x \to 0^-} g(x) =$ 6 (Type an integer or a decimal.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Calculus", "One-Sided Limits" ] }

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Analyze the limit of g(x) as x approaches 0 from the right

Analyze the limit of g(x) as x approaches 0 from the left

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