What is the limit as x approaches 1 of (x^4+x^2-2)/(x^2+2x-3) ?

The limit as x approaches 1 of (x^4+x^2-2)/(x^2+2x-3) is 3/2

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limit as x approaches 1 of (x^4+x^2-2)/(x^2+2x-3)

x \to 1 lim (\frac{x ^{4} + x ^{2} - 2}{x ^{2} + 2 x - 3})

\frac{3}{2}

Decimal Notation

1.5

Solution steps

x \to 1 lim (\frac{x ^{4} + x ^{2} - 2}{x ^{2} + 2 x - 3})

Simplify

\frac{x ^{4} + x ^{2} - 2}{x ^{2} + 2 x - 3} : \frac{( x + 1 ) ( x ^{2} + 2 )}{x + 3}

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

Plug in the value

x = 1

= \frac{( 1 + 1 ) ( 1 ^{2} + 2 )}{1 + 3}

Simplify

\frac{( 1 + 1 ) ( 1 ^{2} + 2 )}{1 + 3} : \frac{3}{2}

= \frac{3}{2}

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

x \to 0 lim (2 e^{x} cos (x))

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

x \to 0 lim (tan (sin (x)))

x \to - 1 lim (x + 6)

What is the limit as x approaches 1 of (x^4+x^2-2)/(x^2+2x-3) ?
The limit as x approaches 1 of (x^4+x^2-2)/(x^2+2x-3) is 3/2