Finding Limit \(\displaystyle\lim_{{{x}\to\infty}}{\left({2}^{{x}}+{3}^{{x}}+{5}^{{x}}+{7}^{{x}}+{11}^{{x}}+{13}^{{x}}\right)}^{{{\frac{{{1}}}{{{x}}}}}}\)

Aiyana Ayers

Aiyana Ayers

Answered question

2022-04-08

Finding Limit
limx(2x+3x+5x+7x+11x+13x)1x

Answer & Explanation

Frain4i62

Frain4i62

Beginner2022-04-09Added 16 answers

From the idea in the question here, for x>0
13x<2x+3x+5x+7x+11x+13x<613x
whence
13<(2x+3x+5x+7x+11x+13x)1x<61x13
Now use the squeeze theorem.

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