How do you find the derivative of h(s)=3+23s using the limit process?

Explanation:dh(s)ds=limk→0h(s+k)−h(s)k=limk→0(3+23(s+k))−(3+23s)k=limk→023kk=limk→023=23

Expert Answer to "How do you find the derivative of h(s)=3+23s..."

High School
Calculus and Analysis
Calculus 1
Derivatives

Jasiah Vincent

Answered question

2022-04-14

How do you find the derivative of

h (s) = 3 + \frac{2}{3} s

using the limit process?

Answer & Explanation

Nico Buck

Beginner2022-04-15Added 9 answers

Explanation:
$\frac{d h (s)}{d s} = lim_{k \to 0} \frac{h (s + k) - h (s)}{k}$
$= lim_{k \to 0} \frac{(3 + \frac{2}{3} (s + k)) - (3 + \frac{2}{3} s)}{k}$
$= \lim_{k \to 0} \frac{\frac{2}{3} k}{k}$
$= lim_{k \to 0} \frac{2}{3}$
$= \frac{2}{3}$

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