How To Solve Limits How To Solve Limits

1. If a function is a simple function, f(x) at x=a, then simply put the value of x=a in the function and solve it. 2. If the function f(x) is any rational number, then factorize the given function, find what is common in numerator and denominator, cancel them and solve for the value of x. 3. If the function is a surd, then to simplify for any value x=a, we first multiply the numerator and denominator by its conjugate surd. Now, we simplify And find the value of the function for x=a. 4. If the given function is a series, which can be expanded, then simply expand it, simplify it and cancel common numerator and denominator then, substitute the value of x=a to get the solution. Know More About Inverse Function Worksheet

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Example 1: The graph below shows that as x approaches 1 from the left, y = f(x) approaches 2 and this can be written as limx→1- f(x) = 2 As x approaches 1 from the right, y = f(x) approaches 4 and this can be written as limx→1+ f(x) = 4 Note that the left and right hand limits and f(1) = 3 are all different. Example 2: This graph shows that limx→1- f(x) = 2 As x approaches 1 from the right, y = f(x) approaches 4 and this can be written as limx→1+ f(x) = 4 Note that the left hand limit and f(1) = 2 are equal. Example 3: This graph shows that Read  More About Verifying Trigonometric Identities Worksheet

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limx→0- f(x) = 1 and limx→0+ f(x) = 1 Note that the left and right hand limits are equal and we cvan write limx→0 f(x) = 1 In this example, the limit when x approaches 0 is equal to f(0) = 1. Example 4: This graph shows that as x approaches - 2 from the left, f(x) gets smaller and smaller without bound and there is no limit. We write limx→-2- f(x) = - ∞ As x approaches - 2 from the right, f(x) gets larger and larger without bound and there is no limit. We write limx→-2+ f(x) = + ∞ Note that - ∞ and + ∞ are symbols and not numbers. These are symbols used to indicate that the limit does not exist.

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How To Solve Limits

1. If a function is a simple function, f(x) at x=a, then simply put the value of x=a in the function and solve it. 2. If the function f(x) i...