$\frac{\Delta y}{\Delta x}$ ? No, $\theta$ .

Calculus Level 3

What is a function $g(x)$ which outputs $\theta$ when $\Delta x$ approaches 0?

f'(\arctan(x))

\frac{\arcsin(f'(x))}{\arccos(f'(x))}

\arcsin(\arccos(f'(x)))

\arctan(f(x))

\arctan(f'(x))

1 solution

Andrei Li
Aug 3, 2018

The key is to recognize that $\tan(\theta)=\frac{\Delta y}{\Delta x}$ , which, as $\Delta x\to0$ , gives $\tan(\theta)=f'(x)$ or $\theta=\arctan{f'(x)}$ This angle $\theta$ is called the incline .

Δ y Δ x \frac{\Delta y}{\Delta x} Δ x Δ y ​ ? No, θ \theta θ .

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$\frac{\Delta y}{\Delta x}$ ? No, $\theta$ .