limit as x approaches 0+of 3x^{sqrt(x)}

解答

x \to 0 + lim (3 x^{x})

3

求解步骤

x \to 0 + lim (3 x^{x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to 0 + lim (x^{x})

使用指数运算法则

= 3 \cdot x \to 0 + lim (e^{x l n (x)})

使用极限链式法则:

1

= 3 \cdot 1

化简

= 3

2 x^{2} y^{^{''}} + 6 x y^{^{'}} + 2 y = 0, y (1) = 2, y^{^{'}} (1) = - 1

y^{^{''}} - 6 y^{^{'}} + 9 y = 2 t e^{3 t}

x \to 2 - lim (\frac{4}{( x - 2 ) ^{5}})

y^{^{'}} - y = 4 sin (3 t)

in v erse l a pl a ce \frac{1}{s - 1}