What is the limit as h(x) approaches 0 of (x+h(x))^n ?

The limit as h(x) approaches 0 of (x+h(x))^n is x^n

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limit as h(x) approaches 0 of (x+h(x))^n

h (x) \to 0 lim ((x + h (x))^{n})

x^{n}

Solution steps

h (x) \to 0 lim ((x + h (x))^{n})

Plug in the value

h (x) = 0

, assuming the function is continuous at this point

= (x + 0)^{n}

Simplify

= x^{n}

x \to 2 lim (\frac{x ^{2} + 5 x - 14}{x ^{2} - 11 x + 18})

x \to - 1 lim (4 x + 3)

x \to - 1 lim (\frac{7 x + 3}{x + 1})

x \to c lim (5 x^{2} + b)

x \to 0 + lim (6 x ln (x))

What is the limit as h(x) approaches 0 of (x+h(x))^n ?
The limit as h(x) approaches 0 of (x+h(x))^n is x^n