When x → 0, y → 1, find LIM (1-xy) / X & # 178; + Y & # 178;

When x → 0, y → 1, find LIM (1-xy) / X & # 178; + Y & # 178;

lim(1-xy)/x²+y²
=lim(1-0)/0+1
=1

Find Lim sin (XY) / XY, X tends to 2, y tends to 0

First of all, you need to know the limit value: LIM (s - > 0) sin s / S = LIM (s - > 0) cos s / 1 = cos 0 = 1 (using the lobita rule) LIM (x - > 2, Y - > 0) sin (XY) / XY = LIM (Y - > 0) sin (2Y) / (2Y) (substitution 2Y = s) = LIM (s - > 0) sin s / S = 1

Lim [(x ^ 2 + x-1) ^ 1 / 2 - (x ^ 2-2x + 3) ^ 1 / 2] when x tends to negative infinity

Take it as a fraction [(x ^ 2 + x-1) ^ 1 / 2 - (x ^ 2-2x + 3) ^ 1 / 2] and multiply it up and down at the same time [(x ^ 2 + x-1) ^ 1 / 2 + (x ^ 2-2x + 3) ^ 1 / 2] to (3x-4) \ [(x ^ 2 + x-1) ^ 1 / 2 + (x ^ 2-2x + 3) ^ 1 / 2]. In this case, the numerator denominator is divided by X at the same time, numerator = 3-4, denominator = 2