LIM (x → 0) for X & # 178; e ^ (1 / X & # 178;)

LIM (x → 0) for X & # 178; e ^ (1 / X & # 178;)

Let x = 1 / T
Original formula = LIM (T - > + ∞) e ^ t / T
=lim(t->+∞)e^t/1
=+∞

lim(x+1）\（x²—x—2) x→2

x→2
lim(x+1）/（x²—x—2)
=lim(x+1)/[(x+1)(x-2)]
=lim 1/(x-2)
=∞ (does not exist)

LIM (Sin & # 178; x-x & # 178; cosx)) / (X & # 178; ln (1 + x) arcsinx) when x approaches 0

Using the law of lobita, the equivalent infinitesimal is solved

When x tends to positive infinity, LIM (√ (X & # 178; + x) - √ (X & # 178; - x))
lim(√(x²+x)-√(x²-x))

The molecule is rationalized, (2x) / (√ (X & # 178; + x) + √ (X & # 178; - x)), and then divided by X, the final result is 1