Find y = (e ^ x-x-1) / (x ^ 2) limit? (x tends to 0) Such as title

Find y = (e ^ x-x-1) / (x ^ 2) limit? (x tends to 0) Such as title

Let x = 1 / T, then t tends to 0 and becomes the original formula
lim[1/t-ln(1+t)/t^2]=lim[t-ln(1+t)]/t^2
=Lim [1-1 / (1 + T)] / 2T (ropida's law)
=lim1/2(1+t)=1/2

Find the limit of 1 / 1 + e ^ 1 / X when x tends to 0 How to analyze when x tends to 0 - and 0 +

When x tends to 0 -, 1 / X is negative infinity, the negative infinity of E is 0, and the answer is 1
When x tends to 0 +, 1 / X is positive infinity, the original formula is one infinity, and the answer is 0

When x tends to 0, find the limit of (x + e ^ x) ^ (1 / x)

1 ^∞ formula
Assuming that limf (x) ^ (g (x)) is of type 1 ^∞, the limit of the original formula of limg (x) [f (x) - 1] = a is e ^ a
LIM (X -- > 0) (e ^ X-1 + x) / x = 2, so the original limit is e ^ 2

X tends to be 0, 0 × What is the limit of 1 / x?

0 times any number equals 0
So the result is 0
0 must be 0 and cannot be 0

[(1 / X of 2 + e) / (2 / X of 1 + e) + |x| / x] limit when x tends to 0

(x->0)lim[2+e^(1/x)]/[(1+e^(2/x)] + |x|/x
=(T - > ∞) LIM (2 + e ^ t) / (1 + e ^ 2t) + T / |t| transformation variable t = 1 / X
=(t->∞)lim(2/e^t+1)/(1/e^t+e^t) + t/|t|
=(t->∞)lim 1/e^t + t/|t|
=(t->∞)lim t/|t|
T - > + ∞, original formula = 1
T - > - ∞, original formula = - 1
Therefore, the original formula has no limit

Find the limit of x ^ 2 * e ^ 1 / X when x tends to 0

Let t = 1 / x, X - > 0, T - > ∞ LIM (x - > 0) X ² / e^(1/x) = lim(t->∞ ) e^(-t) / t ² lim(x->0+) x ² / e^(1/x) = lim(t->+∞ ) e^(-t) / t ² = 0lim(x->0-) x ² / e^(1/x) = lim(t->-∞ ) e^(-t) / t&#...