What is the limit as n approaches 1 of nx(1-x^2)^n ?

The limit as n approaches 1 of nx(1-x^2)^n is x(1-x^2)

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limit as n approaches 1 of nx(1-x^2)^n

n \to 1 lim (n x (1 - x^{2})^{n})

x (1 - x^{2})

Solution steps

n \to 1 lim (n x (1 - x^{2})^{n})

Plug in the value

n = 1

= 1 \cdot x (1 - x^{2})^{1}

Simplify

= x (1 - x^{2})

x \to 0 lim (\frac{( 4 x - x ^{2} )}{x})

x \to - 2 lim (3 x^{3} + x - 2021)

x \to 0 + lim ((1 - x)^{l n (x)})

x \to 0 + lim (\frac{7}{x} - ln (x))

x \to 0 lim (\frac{3 ^{1 - \frac{1}{x}} - 2}{3 ^{- \frac{1}{x}} + 1})

What is the limit as n approaches 1 of nx(1-x^2)^n ?
The limit as n approaches 1 of nx(1-x^2)^n is x(1-x^2)