If f(x) = sin x + cos x,then fleft(frac{pi}{4 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $f(x) = \sin x + \cos x$. First derivative: $f'(x) = \cos x - \sin x$. Second derivative: $f''(x) = -\sin x - \cos x$. Third derivative: $f'

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Given $f(x) = \sin x + \cos x$. First derivative: $f'(x) = \cos x - \sin x$. Second derivative: $f''(x) = -\sin x - \cos x$. Third derivative: $f'''(x) = -\cos x + \sin x$. Fourth derivative: $f^{(iv)}(x) = \sin x + \cos x$. Now,evaluate at $x = \frac{\pi}{4}$: $f\left(\frac{\pi}{4}ight) = \sin\left(\frac{\pi}{4}ight) + \cos\left(\frac{\pi}{4}ight) = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2}$. Similarly,$f^{(iv)}\left(\frac{\pi}{4}ight) = \sin\left(\frac{\pi}{4}ight) + \cos\left(\frac{\pi}{4}ight) = \sqrt{2}$. Therefore,$f\left(\frac{\pi}{4}ight) f^{(iv)}\left(\frac{\pi}{4}ight) = \sqrt{2} 	imes \sqrt{2} = 2$.

If $f(x) = \sin x + \cos x$,then $f\left(\frac{\pi}{4}\right) f^{(iv)}\left(\frac{\pi}{4}\right)$ is equal to

Similar Questions

On increasing the reverse bias to a large value in a $PN-$junction diode,current

$A$ bulb of $100 \ W$ rating is connected with $220 \ V$ supply. The resistance of the bulb is . . . . . . .

Which is the smallest angiosperm?

Which of the following enzymes hydrolyzes the internal phosphodiester bonds in a polynucleotide chain?

Vedclass Test Series

Exam Paper Generator

Online Exam Module