1.

Making use of the method of replacing an infinitesimal with an equivalent one, find the following limits: underset(x to 0)lim (sin 3x)/(ln (1+5x)) (b) underset(x to 0)lim (ln (1+sin 4x))/(e^(sin 5x)-1) (c ) underset(x to 0) (e^(sin 3x)-1)/(ln (1+tan 2x)) (d) underset(x to 0)lim (arc tan 3x)/(arc sin 2x) (e ) underset(x to 0)lim (ln (2-cos 2x))/(ln^(2) (sin 3x+1)) (f) underset(x to 0)lim (sqrt(1+sin 3x)-1)/(ln (1+tan 2x)) (g) underset(x to 0)lim ln (1+2x-3x^(2)+4x^(3))/(ln (1-x+2x^(2)-7x^(3)) (h) underset(x to 0)lim (sqrt(1+x^(2))-1)/(1-cos x)

Answer»


ANSWER :`(a) 3/5, (b) 4/5, (c) 3/2, (d) 3/2, (E) 2/9, (f) 3/4, (g)-2, (H)1`.


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