What is the limit as t approaches infinity of sqrt(25t^2+2)-5t ?

The limit as t approaches infinity of sqrt(25t^2+2)-5t is 0

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limit as t approaches infinity of sqrt(25t^2+2)-5t

t \to \infty lim (25 t^{2} + 2 - 5 t)

0

Solution steps

t \to \infty lim (25 t^{2} + 2 - 5 t)

Multiply by the conjugate of

25 t^{2} + 2 - 5 t : \frac{2}{25 t ^{2} + 2 + 5 t}

= t \to \infty lim (\frac{2}{25 t ^{2} + 2 + 5 t})

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

= 2 \cdot t \to \infty lim (\frac{1}{25 t ^{2} + 2 + 5 t})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= 2 \cdot \frac{lim _{t \to \infty} ( 1 )}{lim _{t \to \infty} ( 25 t ^{2} + 2 + 5 t )}

t \to \infty lim (1) = 1

t \to \infty lim (25 t^{2} + 2 + 5 t) = \infty

= 2 \cdot \frac{1}{\infty}

Simplify

2 \cdot \frac{1}{\infty} : 0

= 0

y \to 0 - lim (\frac{y}{∣ y ∣})

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

x \to 2 lim (x^{2} - 9)

x \to - \infty lim (9^{x})

x \to 3 + lim ([3 x - 10] + x)

What is the limit as t approaches infinity of sqrt(25t^2+2)-5t ?
The limit as t approaches infinity of sqrt(25t^2+2)-5t is 0