lim((g(x)sin(2x)+e^(2x)-1)/x),x->0,lim g(x)=5,x->0 without using L'Hospital's rule

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lim((g(x)*sin(2x)+e^(2*x)-1)/x),x->0,lim g(x)=5,x->0 without using L'Hospital's rule

Guest Sep 27, 2015

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Guest Sep 28, 2015

Alan · Answer 1 · 2015-09-27T09:12:35

When x → 0, sin(2x) → 2x and e^(2x) → 1 + 2x so (g(x)*sin(2x) + e^(2x) - 1)/x → (5*2x + 1 + 2x - 1)/x → 12x/x → 12

lim((g(x)*sin(2x)+e^(2*x)-1)/x),x->0,lim g(x)=5,x->0 without using L'Hospital's rule