What is the limit as x approaches 0+of-4csc^2(4x) ?

The limit as x approaches 0+of-4csc^2(4x) is -infinity

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limit as x approaches 0+of-4csc^2(4x)

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

- \infty

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= - 4 \cdot x \to 0 + lim (csc^{2} (4 x))

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= - 4 (x \to 0 + lim (csc (4 x)))^{2}

Express with sin, cos

= - 4 (x \to 0 + lim (\frac{1}{sin ( 4 x )}))^{2}

For

x

approaching

0

from the right

, x > 0 \Rightarrow sin (4 x) > 0

The denominator is a positive quantity approaching 0 from the right

= - 4 \infty^{2}

Simplify

- 4 \infty^{2} : - \infty

= - \infty

\int \frac{x - 4}{x ^{2} - x - 6} d x

2 x d y + y d x = 0

\int \frac{4}{x ^{2} + 2 x} d x

\frac{\partial}{\partial x} (x ln (z^{5} + x^{7}))

x y y^{^{'}} + 4 x^{2} + y^{2} = 0

What is the limit as x approaches 0+of-4csc^2(4x) ?
The limit as x approaches 0+of-4csc^2(4x) is -infinity