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hw5 the limit laws (target l4; §2.3)
score: 2/13 answered: 2/13
question 3
evaluate the limit:
\\(\lim_{y\to - 7}(2y - 3)=\\)
question help: video message instructor

Explanation:

Step1: Apply limit - sum/difference rule

$\lim_{y
ightarrow - 7}(2y - 3)=\lim_{y
ightarrow - 7}(2y)-\lim_{y
ightarrow - 7}(3)$

Step2: Apply constant - multiple rule for limits

$\lim_{y
ightarrow - 7}(2y)=2\lim_{y
ightarrow - 7}(y)$

Step3: Evaluate individual limits

We know that $\lim_{y
ightarrow - 7}(y)=-7$ and $\lim_{y
ightarrow - 7}(3) = 3$ (since the limit of a constant function $f(y)=c$ as $y
ightarrow a$ is $c$). Then $2\lim_{y
ightarrow - 7}(y)=2\times(-7)=-14$.

Step4: Calculate the final result

$2\lim_{y
ightarrow - 7}(y)-\lim_{y
ightarrow - 7}(3)=-14 - 3=-17$

Answer:

$-17$