Question

homework2: problem 14 (1 point) evaluate lim_{h→0} (f(5 + h)-f(5))/h, where f(x)=5x + 5. if the limit does not exist enter dne. limit = preview my answers submit answers you have attempted this problem 0 times. you have unlimited attempts remaining. email instructor

Explanation:

Step1: Find \(f(5 + h)\)

Substitute \(x = 5+h\) into \(f(x)=5x + 5\), we get \(f(5 + h)=5(5 + h)+5=25+5h + 5=30 + 5h\).

Step2: Find \(f(5)\)

Substitute \(x = 5\) into \(f(x)=5x + 5\), we get \(f(5)=5\times5 + 5=25 + 5=30\).

Step3: Substitute into the limit expression

\(\lim_{h
ightarrow0}\frac{f(5 + h)-f(5)}{h}=\lim_{h
ightarrow0}\frac{(30 + 5h)-30}{h}\).
Simplify the numerator: \((30 + 5h)-30 = 5h\). So the limit becomes \(\lim_{h
ightarrow0}\frac{5h}{h}\).

Step4: Evaluate the limit

Cancel out the \(h\) terms (\(h
eq0\) as we are taking the limit as \(h\) approaches 0, not setting \(h = 0\)). \(\lim_{h
ightarrow0}\frac{5h}{h}=\lim_{h
ightarrow0}5 = 5\).

Answer:

5