What is the limit as x approaches 0+of 7/x-7|x| ?

The limit as x approaches 0+of 7/x-7|x| is infinity

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limit as x approaches 0+of 7/x-7|x|

x \to 0 + lim (\frac{7}{x} - 7 ∣ x ∣)

\infty

Solution steps

x \to 0 + lim (\frac{7}{x} - 7 ∣ x ∣)

x

is positive when

x \to 0 +

. Therefore

∣ x ∣ = x

= x \to 0 + lim (\frac{7}{x} - 7 x)

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to 0 + lim (\frac{7}{x}) - x \to 0 + lim (7 x)

x \to 0 + lim (\frac{7}{x}) = \infty

x \to 0 + lim (7 x) = 0

= \infty - 0

Apply Infinity Property:

\infty - c = \infty

= \infty

\frac{1}{x - 1}, 12

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

y = x^{3}, x = y^{2}

\int ln (\frac{x}{x ^{2}}) d x

f (x) = \frac{cos ( x )}{x}

What is the limit as x approaches 0+of 7/x-7|x| ?
The limit as x approaches 0+of 7/x-7|x| is infinity