1) lim x->2 ... (2-sqrt(6-x))/(1-sqrt(3-x))
2) lim x->0 ... (3t^2 + sin(t))/(e^t - 1 + 2t)
3) lim x->0 ... (sqrt(x) - 1)/(r^(3/2) - 1)
Am having difficulty finding these limits, any help would be appreciated. thanks.
2) lim x->0 ... (3t^2 + sin(t))/(e^t - 1 + 2t)
3) lim x->0 ... (sqrt(x) - 1)/(r^(3/2) - 1)
Am having difficulty finding these limits, any help would be appreciated. thanks.
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I'm hoping that you are familiar with L'Hopital's rule, because that is what I'm
going to use for each of these:
1.) lim(x->2)((2-sqrt(6-x))/(1-sqrt(3-x))) = lim(x->2)((1/(2sqrt(6-x))) / (1/(2sqrt(3-x))) =
lim(x->2)(sqrt(3-x) / sqrt(6-x)) = 1/2.
2.) lim(t->0)((3t^2 + sin(t))/(e^t-1+2t)) = lim(t->0)((6t + cos(t))/(e^t + 2)) = 1/3.
3.) lim(x->0)((sqrt(x) - 1)/(x^(3/2) - 1) = -1/(-1) = 1. I think you meant
lim(x->1)((sqrt(x) -1)/(x^(3/2) - 1) = lim(x->1)((1/(2sqrt(x)))/((3/2)sqrt(x)) =
lim(x->1)(1/(3x)) = 1/3.
going to use for each of these:
1.) lim(x->2)((2-sqrt(6-x))/(1-sqrt(3-x))) = lim(x->2)((1/(2sqrt(6-x))) / (1/(2sqrt(3-x))) =
lim(x->2)(sqrt(3-x) / sqrt(6-x)) = 1/2.
2.) lim(t->0)((3t^2 + sin(t))/(e^t-1+2t)) = lim(t->0)((6t + cos(t))/(e^t + 2)) = 1/3.
3.) lim(x->0)((sqrt(x) - 1)/(x^(3/2) - 1) = -1/(-1) = 1. I think you meant
lim(x->1)((sqrt(x) -1)/(x^(3/2) - 1) = lim(x->1)((1/(2sqrt(x)))/((3/2)sqrt(x)) =
lim(x->1)(1/(3x)) = 1/3.