Learn how to solve limits by direct substitution problems step by step online. Find the limit of sin(1/x) as x approaches 0. Because sine is a continuous function, we can bring the limit inside of the sine. 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:.

Find the limit of sin(1/x) as x approaches 0