What is the limit as x approaches 2 of x^3-5x^2+7x+1 ?

The limit as x approaches 2 of x^3-5x^2+7x+1 is 3

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limit as x approaches 2 of x^3-5x^2+7x+1

x \to 2 lim (x^{3} - 5 x^{2} + 7 x + 1)

3

Solution steps

x \to 2 lim (x^{3} - 5 x^{2} + 7 x + 1)

Plug in the value

x = 2

= 2^{3} - 5 \cdot 2^{2} + 7 \cdot 2 + 1

Simplify

2^{3} - 5 \cdot 2^{2} + 7 \cdot 2 + 1 : 3

= 3

x \to 0 + lim ((1 + 4 x)^{\frac{1}{x}})

x \to 0 - lim ((1 + 4 x)^{\frac{3}{x}})

x \to 3 lim (x^{3} + 5 x - 1)

x \to 0 lim ((e^{x} + x)^{\frac{7}{x}})

x \to 3 lim (\frac{x ^{2} - 6 x - 9}{x - 3})

What is the limit as x approaches 2 of x^3-5x^2+7x+1 ?
The limit as x approaches 2 of x^3-5x^2+7x+1 is 3