Evaluating the Left-Side Limit of f(x) = 1/x as x Approaches 0 | Understanding the Behavior of the Function

lim x->0- (1/x)

To evaluate the limit as x approaches 0 from the left side of the function f(x) = 1/x, we substitute values that approach 0 from the left side into the function and observe the values of f(x)

To evaluate the limit as x approaches 0 from the left side of the function f(x) = 1/x, we substitute values that approach 0 from the left side into the function and observe the values of f(x).

As x gets closer and closer to 0, but remains negative (left side approaching 0), the values of x become larger in magnitude, meaning they move further away from 0 in the negative direction.

Let’s evaluate the function for some values approaching 0 from the left side:
f(-0.1) = 1/(-0.1) = -10
f(-0.01) = 1/(-0.01) = -100
f(-0.001) = 1/(-0.001) = -1000

We can observe that as x approaches 0 from the left side, the function values become increasingly negative and decrease in magnitude (absolute value). In fact, no matter how large the value of x gets (negative but close to 0), the function value will approach negative infinity.

Therefore, the limit of f(x) = 1/x as x approaches 0 from the left side is negative infinity.

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