Replacing x by −x leaves x² and |x| unchanged, so sin(x²) and exp(−|x|) are even, C and D. The product x|x| changes sign. Cosine is even but division by x makes cos(x)/x odd on its domain excluding zero. Thus A and B are not even.
More Calculus questions
GATE 2022 BM Q51– Using the divergence theorem, evaluate outward flux S F n\,dA across the closed surface of…
GATE 2021 BM Q12– For V(x,y)=(x2+y2)/2, find its directional derivative at (1,1) in direction 3y i-3x j.
GATE 2021 BM Q31– Find the minimum of f(x 1,x 2,x 3)=12(x 12+x 22+x 32)-2(x 1+x 2+x 3), rounded to the…
GATE 2020 BM Q19– Which functions are odd? P=sin t, Q=cos t, R=sin t+cos t, S=sin t cos t.
GATE 2020 BM Q55– Find the magnitude of the gradient of f(x,y)=x²+y² at (1,1), to two decimals.
GATE 2020 BM Q56– Evaluate Rxy\,dx\,dy over the first-quadrant part of the unit disc, to three decimals.