If f is continuous at c, then limx →c^+ f(x)=. (a) limx →c^- f(x) (b) limx →c f(x) (c) f(c) (d)

step 1 Hello, if f is continuous at C then limit X tends to C plus fx is equals to f of C okay if funct

If f is continuous at c, then limx →c^+ f(x)=. (a) limx →c^-...

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Key Concepts

Continuity at a Point

Continuity at a point c means that the function f does not exhibit any abrupt changes at that point. Formally, a function is continuous at c if the limit as x approaches c exists and is equal to the function’s value, i.e., lim??c f(x) = f(c). This definition inherently incorporates both one-sided limits matching the function value when they are considered.

Limit of a Function

The limit of a function as x approaches a particular value c is the value that f(x) gets arbitrarily close to as x nears c. This concept is fundamental in understanding the behavior of functions near points of interest, especially in contexts where the function might not be explicitly defined at the point but still exhibits a predictable pattern nearby.

One-Sided Limits

One-sided limits involve considering the behavior of a function as x approaches a point from only one side; for instance, the right-hand limit (x ? c?) examines the behavior as x approaches c from values greater than c. When a function is continuous at the point c, both the right-hand limit and the left-hand limit equal the actual function value f(c), ensuring consistency across both directions.

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