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Lim x→π/4(sin x-cos x)/(x-fracπ4) is equal to Single correct option
lim x → π / 4 sin x − cos x x − π 4 \displaystyle\lim_{x\to\pi/4}\frac{\sin x-\cos x}{x-\frac\pi4} x → π /4 lim x − 4 π sin x − cos x is equal to
A. 1 1 1 B. 2 \sqrt2 2 C. 0 0 0 D. 1 2 \frac{1}{\sqrt2} 2 1 Show answer and solution Answer: (B) 2 \sqrt2 2
At
x = π 4 x=\frac\pi4 x = 4 π the numerator is
0 0 0 , so the limit is the derivative of
sin x − cos x \sin x-\cos x sin x − cos x at
π 4 \frac\pi4 4 π , namely
cos x + sin x = 1 2 + 1 2 = 2 \cos x+\sin x=\frac{1}{\sqrt2}+\frac1{\sqrt2}=\sqrt2 cos x + sin x = 2 1 + 2 1 = 2 . L'Hospital's rule gives the same. The value
1 2 \frac1{\sqrt2} 2 1 keeps only one of the two terms.
Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake