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The limit of a sum of two or more functions is equal to the sum of the limits of each function: $\displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x))$
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$\lim_{x\to0}\left(\frac{1}{x}\right)+\lim_{x\to0}\left(-\cot\left(x\right)\right)$
Learn how to solve simplification of algebraic expressions problems step by step online. Find the limit of 1/x-cot(x) as x approaches 0. The limit of a sum of two or more functions is equal to the sum of the limits of each function: \displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x)). Evaluate the limit \lim_{x\to0}\left(\frac{1}{x}\right) by replacing all occurrences of x by 0. An expression divided by zero tends to infinity. As by directly replacing the value to which the limit tends, we obtain an indeterminate form, we must try replacing a value close but not equal to 0. In this case, since we are approaching 0 from the left, let's try replacing a slightly smaller value, such as -0.00001 in the function within the limit:.