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 solve this problem, we need to apply the limit property known as the product rule
To solve this problem, we need to apply the limit property known as the product rule. The product rule states that if the limit of two functions exists individually, then the limit of their product is equal to the product of their limits.
Given that lim(x→4) g(x) = 2 and lim(x→4) f(x)g(x) = π, we want to find lim(x→4) f(x).
Using the product rule, we can rewrite the equation:
lim(x→4) f(x)g(x) = lim(x→4) f(x) * lim(x→4) g(x) = π
We know that lim(x→4) g(x) = 2, so substituting this value into the equation, we get:
lim(x→4) f(x) * 2 = π
To find lim(x→4) f(x), we can divide both sides of the equation by 2:
lim(x→4) f(x) = π/2
Therefore, the limit of f(x) as x approaches 4 is π/2.
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