What is the limit as x approaches infinity of 1+x^{(-1)/2}+x^{(-2)/3}+x^{(1-x)/x} ?

The limit as x approaches infinity of 1+x^{(-1)/2}+x^{(-2)/3}+x^{(1-x)/x} is 1

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limit as x approaches infinity of 1+x^{(-1)/2}+x^{(-2)/3}+x^{(1-x)/x}

x \to \infty lim (1 + x^{\frac{- 1}{2}} + x^{\frac{- 2}{3}} + x^{\frac{1 - x}{x}})

1

Solution steps

x \to \infty lim (1 + x^{\frac{- 1}{2}} + x^{\frac{- 2}{3}} + x^{\frac{1 - x}{x}})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim (1) + x \to \infty lim (x^{\frac{- 1}{2}}) + x \to \infty lim (x^{\frac{- 2}{3}}) + x \to \infty lim (x^{\frac{1 - x}{x}})

x \to \infty lim (1) = 1

x \to \infty lim (x^{\frac{- 1}{2}}) = 0

x \to \infty lim (x^{\frac{- 2}{3}}) = 0

x \to \infty lim (x^{\frac{1 - x}{x}}) = 0

= 1 + 0 + 0 + 0

Simplify

= 1

x \to 1 + lim (\frac{x ^{2}}{ln ( x )})

x \to 1 lim (- 8)

x \to \frac{π}{2} lim ((sin^{2} (x))^{t a n (x)})

x \to - 1 lim (7)

x \to - 3 lim (\frac{x ^{2} - 2}{x - 4})

What is the limit as x approaches infinity of 1+x^{(-1)/2}+x^{(-2)/3}+x^{(1-x)/x} ?
The limit as x approaches infinity of 1+x^{(-1)/2}+x^{(-2)/3}+x^{(1-x)/x} is 1