How do you find the limit of ( e^(3t) - 1 ) / t as x approaches 0? Calculus Limits Determining Limits Algebraically 1 Answer Cesareo R. May 28, 2016 3 Explanation: We will be using e^x= sum_{n=0}^{infty}x^n/(n!) Taking e^{3t} = 1 + 3t+(3t)^2/2+(3t)^3/6+... and substituting lim_{t->0}(e^{3t}-1)/t = lim_{t->0}((1+ 3t+(3t)^2/2+(3t)^3/6+...-1)/t) lim_{t->0}(e^{3t}-1)/t =lim_{t->0}(t((3+(3t)/2+(3t)^2/6+...))/t)=3 Answer link Related questions How do you find the limit lim_(x->5)(x^2-6x+5)/(x^2-25) ? How do you find the limit lim_(x->3^+)|3-x|/(x^2-2x-3) ? How do you find the limit lim_(x->4)(x^3-64)/(x^2-8x+16) ? How do you find the limit lim_(x->2)(x^2+x-6)/(x-2) ? How do you find the limit lim_(x->-4)(x^2+5x+4)/(x^2+3x-4) ? How do you find the limit lim_(t->-3)(t^2-9)/(2t^2+7t+3) ? How do you find the limit lim_(h->0)((4+h)^2-16)/h ? How do you find the limit lim_(h->0)((2+h)^3-8)/h ? How do you find the limit lim_(x->9)(9-x)/(3-sqrt(x)) ? How do you find the limit lim_(h->0)(sqrt(1+h)-1)/h ? See all questions in Determining Limits Algebraically Impact of this question 4487 views around the world You can reuse this answer Creative Commons License