Learn how to solve differential equations problems step by step online. Find the limit of (2^x+1)/(2^x-x) as x approaches infinity. The limit of the quotient of two functions is the quotient of their limits. Evaluate the limit \lim_{x\to\infty }\left(2^x+1\right) by replacing all occurrences of x by \infty . The limit of a polynomial function (2^x-x) when x tends to infinity is equal to the limit of it's highest degree term (the term that when i'ts evaluated at a high value, grows quickier to infinity), so it's solution is equivalent to calculating the limit of only the highest degree term. Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}.

Find the limit of (2^x+1)/(2^x-x) as x approaches infinity