Help pls (1 Viewer)

Run hard@thehsc · Apr 7, 2022

Can someone help me with the question above?

5uckerberg · Apr 7, 2022

I assume the question refers to $x\cos^{-1}\left(2x\right)-\sqrt{1-x^{2}}$ at $x=\frac{1}{4}$

First step,
$\frac{d}{dx}\left(x\cos^{-1}\left(2x\right)-\sqrt{1-x^{2}}\right)$
$\cos^{-1}\left(2x\right)-\frac{2x}{\sqrt{1-4x^{2}}}+\frac{x}{\sqrt{1-x^{2}}$
Step 2 sub in $x=\frac{1}{4}$
$\cos^{-1}\left(\frac{1}{2}\right)-\frac{\frac{1}{2}}{\sqrt{\frac{3}{4}}}+\frac{\frac{1}{4}}{\sqrt{\frac{15}{16}}$
$\frac{\pi}{3}-\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{15}}$
$\frac{\sqrt{15}\pi-3\sqrt{5}+3}{3\sqrt{15}}$
$\frac{15\pi-15\sqrt{3}+3\sqrt{15}}{45}$
$m\approx{0.73}$
$y-\left(\frac{\pi}{12}-\frac{\sqrt{15}}{4}\right)=\frac{\sqrt{15}\pi-3\sqrt{5}+3}{3\sqrt{15}}\left(x-\frac{1}{4}\right)$
Intercept is $\left(\frac{\pi}{12}-\frac{\sqrt{15}}{4}\right)-\frac{\sqrt{15}\pi-3\sqrt{5}+3}{12\sqrt{15}}$
$\frac{\sqrt{15}\pi-45-\left(\sqrt{15}\pi-3\sqrt{5}+3\right)}{12\sqrt{15}}$
$\frac{-48+3\sqrt{5}}{12\sqrt{15}}$
$\frac{-4}{\sqrt{15}}+\frac{1}{4\sqrt{3}}$
$b\approx{-0.60}$

Help pls (1 Viewer)

Run hard@thehsc

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5uckerberg

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