homework2: problem 14 (1 point) evaluate lim_{h→0} (f(5 + h)-f(5))/h, where f(x)=5x + 5. if the limit does…

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

Answer

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\rightarrow0}\frac{f(5 + h)-f(5)}{h}=\lim_{h\rightarrow0}\frac{(30 + 5h)-30}{h}). Simplify the numerator: ((30 + 5h)-30 = 5h). So the limit becomes (\lim_{h\rightarrow0}\frac{5h}{h}).

Step4: Evaluate the limit

Cancel out the (h) terms ((h\neq0) as we are taking the limit as (h) approaches 0, not setting (h = 0)). (\lim_{h\rightarrow0}\frac{5h}{h}=\lim_{h\rightarrow0}5 = 5).