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f(x)=x/(e^(6x))−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

lim⁡x→∞ (xe6x)\lim_{x\to\infty\:}\left(\frac{x}{e^{6x}}\right)

Step-by-step Solution

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Because polynomial functions (xx) grow asymptotically slower than exponential functions (e6xe^{6x}), we can say that the expression lim⁡x→∞(xe6x)\lim_{x\to\infty }\left(\frac{x}{e^{6x}}\right) tends to zero as xx goes to infinity

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limx→∞ (xe6x )
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