What is the limit as r approaches 1 of (sqrt((r^2+3r-2)^3))/(sqrt((5r-3)^2)) ?

The limit as r approaches 1 of (sqrt((r^2+3r-2)^3))/(sqrt((5r-3)^2)) is square root of 2

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limit as r approaches 1 of (sqrt((r^2+3r-2)^3))/(sqrt((5r-3)^2))

r \to 1 lim \frac{( r ^{2} + 3 r - 2 ) ^{3}}{( 5 r - 3 ) ^{2}}

2

Decimal Notation

1.41421 \dots

Solution steps

r \to 1 lim \frac{( r ^{2} + 3 r - 2 ) ^{3}}{( 5 r - 3 ) ^{2}}

Plug in the value

r = 1

= \frac{( 1 ^{2} + 3 \cdot 1 - 2 ) ^{3}}{( 5 \cdot 1 - 3 ) ^{2}}

Simplify

\frac{( 1 ^{2} + 3 \cdot 1 - 2 ) ^{3}}{( 5 \cdot 1 - 3 ) ^{2}} : 2

= 2

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

x \to - 4 lim ((10 x + 36)^{3})

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

x \to 0 lim (\frac{1}{2.5})

x \to \frac{π}{2} lim (sin (2 x + π))

What is the limit as r approaches 1 of (sqrt((r^2+3r-2)^3))/(sqrt((5r-3)^2)) ?
The limit as r approaches 1 of (sqrt((r^2+3r-2)^3))/(sqrt((5r-3)^2)) is square root of 2