Vega Cummings
06/13/2024 · Middle School
Consider the following function, where \( m \) is a parameter. \( f(x)=\left\{\begin{array}{ll}-x^{2}+m x & \text { if } x \leq-3 \\ 2 x+1 & \text { if } x>-3\end{array}\right. \) Evaluate the given limits. Your answers may contain \( m \). If a limit does not exist, enter DNE. (a) \( \lim _{x \rightarrow-3^{-}} f(x)= \) Submit Part
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Tutor-Verified Answer
Step-by-step Solution
Calculate the limit \( \lim_{x\rightarrow -3^{-}} (-x^2 + mx) \).
Evaluate the limit by following steps:
- step0: Evaluate the limit:
\(\lim _{x\rightarrow \left(-3\right)^{-}}\left(-x^{2}+mx\right)\)
- step1: Calculate:
\(\lim _{x\rightarrow -3^{-}}\left(-x^{2}+mx\right)\)
- step2: Rewrite the expression:
\(\lim _{x\rightarrow -3^{-}}\left(-x^{2}\right)+\lim _{x\rightarrow -3^{-}}\left(mx\right)\)
- step3: Calculate:
\(-9-3m\)
The limit \( \lim _{x \rightarrow-3^{-}} f(x) \) is equal to \(-9-3m\).
Quick Answer
\( \lim _{x \rightarrow-3^{-}} f(x)=-9-3m \)
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