Evaluate the limit. lim_x rightarrow infinity 7x^2 + 8x/5x^2 + 6 In general, we

Question

Evaluate the limit. lim_x rightarrow infinity 7x^2 + 8x/5x^2 + 6 In general, we wish to use the Quotient Law to evaluate limits of rational functions. Recall the Quotient Law. If lim_x rightarrow c f(x) and lim_x rightarrow c g(x) exist (as a finite number) and lim_x rightarrow c g(x) notequalto 0, then we have the following equation. lim_x rightarrow c f(x)/g(x) = lim_x rightarrow c f(x)/lim_x rightarrow c g(x) To see if we can directly apply the Quotient Law to evaluate lim_x rightarrow infinity 7x^2 + 8x/5x^2 + 6, use Basic Limit Laws to determine the limit as x approaches infinity of both the numerator and denominator. Recall that lim_x rightarrow infinity x^n = infinity for all n > 0. lim_x rightarrow infinity (7x^2 + 8x) = lim_x rightarrow infinity (5x^2 + 6) = Since both of these limits exist as finite numbers, we directly apply the Quotient Law.

Explanation / Answer

as x tend to infinity, both numerator and denominator is tending to infinity so you have to fill infinity in both the boxes.

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