Question

Find the limits x to pi/4 sinx -cos x / x-pi/4

Answer 1

hope it helps.........!!!!!!!

Answer 2

The value of limits is √2

Step-by-step explanation:

The given limit is

$\lim _{x\to \frac{\pi }{4}}\frac{\left(sinx-cosx\right)}{x-\frac{\pi }{4}}$

Apply L' Hospital's Rule:

$\lim _{x\to \frac{\pi }{4}}\left(\frac{\cos \left(x\right)+\sin \left(x\right)}{1}\right)\\\\=\lim _{x\to \frac{\pi }{4}}\left(\cos \left(x\right)+\sin \left(x\right)\right)$

Now, simplify by substituting the limit value

$\cos \left(\frac{\pi }{4}\right)+\sin \left(\frac{\pi }{4}\right)$

On simplifying, we get

$=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\\\\=\frac{2}{\sqrt{2}}\\\\=\sqrt2$

Therefore, the value of limits is √2

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