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Popular >

limit as x approaches infinity of (sqrt(x+a)+sqrt(x+b))/(sqrt(x))

Solution

x \to \infty lim (\frac{x + a + x + b}{x})

Solution

2

Solution steps

x \to \infty lim (\frac{x + a + x + b}{x})

Expand

\frac{x + a + x + b}{x} : \frac{x + a}{x} + \frac{x + b}{x}

= x \to \infty lim (\frac{x + a}{x} + \frac{x + b}{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 \infty lim (\frac{x + a}{x}) + x \to \infty lim (\frac{x + b}{x})

x \to \infty lim (\frac{x + a}{x}) = 1

x \to \infty lim (\frac{x + b}{x}) = 1

= 1 + 1

Simplify

= 2

Graph

Popular Examples

limit as x approaches 0 of ln(((1+x))/x)

x \to 0 lim (ln (\frac{( 1 + x )}{x}))

limit as x approaches 9 of (x-sqrt(72+x))/(9-x)

x \to 9 lim (\frac{x - 72 + x}{9 - x})

limit as h approaches 2 of 1/(4-h^2)

h \to 2 lim (\frac{1}{4 - h ^{2}})

limit as x approaches infinity of 2+3x

x \to \infty lim (2 + 3 x)

limit as x approaches infinity of 2^x-x

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

Frequently Asked Questions (FAQ)

What is the limit as x approaches infinity of (sqrt(x+a)+sqrt(x+b))/(sqrt(x)) ?
The limit as x approaches infinity of (sqrt(x+a)+sqrt(x+b))/(sqrt(x)) is 2