Question

lim(x->0) cos5x-cos3x/5x^2

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Answer 1

lim (cos(5x)-cos(3x))/(5x^2)=lim (cos(5x)-1 + 1-cos (3x))/(5x^2)=-lim(1-cos(5x))/(5x)^2 *2*(5x)^2/(2*5x^2)+ lim (1-cos(3x))/(3x)^2 *2*(3x)^2/(2*5x^2) =-1 lim (25x^2/10x^2)+ lim (9x^2/10x^2)=-2.5+0.9=-1.6