I am using this book: https://www.amazon.com/Calculus-Int...sr_1_1?ie=UTF8&s=books&qid=1275951079&sr=1-1"(adsbygoogle = window.adsbygoogle || []).push({});

Calculus: An Intuitive and Physical Approach by: Kline

I've already finished Calc I and II, but I'm brushing up on my skills because I don't feel entirely confident about them.

This is what the method says to do to find a derivative:

[tex]s = 10t^2[/tex] given [tex]t=3[/tex]

[tex]s_{3} + \Delta s = 10(3 + \Delta t)^2[/tex]

[tex]s_{3} + \Delta s = 90 + 60\Delta t + 10\Delta t^2[/tex]

[tex] - (s_{3} = 90) [/tex]

[tex]\frac{\Delta s}{\Delta t} = \frac{60 \Delta t + 10 \Delta t^2}{\Delta t}[/tex]

[tex]\displaystyle{\frac{\Delta s}{\Delta t}} = 60 + 10 \Delta t [/tex]

[tex]lim_{\Delta t \rightarrow 0} \displaystyle{\frac{\Delta s}{\Delta t}} = 60[/tex]

I understand the method and have finished all of the practice problems in the book, but I'm having trouble linking this with the way I was taught to derive in my calculus class with

[tex]lim_{h \rightarrow 0} \frac{f(a + h) - f(a)}{h}[/tex]

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# Method of Increments?

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