Find the limit: Limit as h approaches 0^+ of (sqrt(h^2 + 12h + 5) - sqrt(5))/h.


Find the limit: {eq}\; \lim_{h\rightarrow 0^+}\frac{\sqrt{h^2 + 12h + 5} - \sqrt{5}}{h} {/eq}.


We have a fraction inside the limit. If we try direct plugging in the value of zero, we get an undefined limit of zero over zero. We calculate such limits by applying the L'Hospital's rule or using other algebraic tools.

Answer and Explanation:

The value of this fraction at {eq}\; h =0 \; {/eq} is 0/0 so we have an indeterminate form .

We multiply both the numerator and the denominator of...

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