What is the limit as x approaches 0 of (csc^2(x))/(cot^2(x)) ?

The limit as x approaches 0 of (csc^2(x))/(cot^2(x)) is 1

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limit as x approaches 0 of (csc^2(x))/(cot^2(x))

x \to 0 lim (\frac{csc ^{2} ( x )}{cot ^{2} ( x )})

1

Solution steps

x \to 0 lim (\frac{csc ^{2} ( x )}{cot ^{2} ( x )})

Simplify

\frac{csc ^{2} ( x )}{cot ^{2} ( x )} : sec^{2} (x)

= x \to 0 lim (sec^{2} (x))

Plug in the value

x = 0

= sec^{2} (0)

Simplify

sec^{2} (0) : 1

= 1

x \to \infty lim (\frac{6 x ^{2} - 7 x + 10}{5 x ^{3} + 2 x ^{2} - 4 x + 5})

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

x \to 2 - lim (x (2))

x \to \infty lim (\frac{2 x}{7})

x \to - 8 lim (x)

What is the limit as x approaches 0 of (csc^2(x))/(cot^2(x)) ?
The limit as x approaches 0 of (csc^2(x))/(cot^2(x)) is 1