Finding the Value of limx→4f(x) Using Algebraic Manipulation: Step-by-Step Guide and Solution

Let ff and gg be functions such that limx→4g(x)=2limx→4g(x)=2 and limx→4f(x)g(x)=πlimx→4f(x)g(x)=π. What is limx→4f(x)limx→4f(x) ?

To find the value of limx→4f(x), we can use the following algebraic manipulation

To find the value of limx→4f(x), we can use the following algebraic manipulation.

Given: limx→4g(x) = 2

We are also given that limx→4f(x)g(x) = π.

We can rewrite the second given expression as:

limx→4f(x) * limx→4g(x) = π

Now, we can substitute the value of limx→4g(x) from the first given expression:

limx→4f(x) * 2 = π

To find limx→4f(x), we can isolate it by dividing both sides by 2:

limx→4f(x) = π/2

Therefore, the value of limx→4f(x) is π/2.

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