Suppose f and g are continuous functions such that g(4)=6 and lim x->4 [3f(x)+f(x)g(x)] = 45. Find f(4). ... (How do I begin
solving this problem? Step by step assist please)
1 answer:
Answer:
The value of f(4) is 5. We can write f(4) = 5.
Step-by-step explanation:
Since it is given that
![\lim_{x\rightarrow 4}[3f(x)+f(x)g(x)]=45](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Crightarrow%204%7D%5B3f%28x%29%2Bf%28x%29g%28x%29%5D%3D45)
This is only possible if both the functions f(x) and g(x) are continuous at x = 4.
Now since the functions are continuous at x = 4 they need to be defined at the said value in accordance with the definition of continuous function.
Thus to obtain the limit we just put x = 4 in left hand side of the given relation thus getting
![[3f(4)+f(4)g(4)]=45..........(i)](https://tex.z-dn.net/?f=%5B3f%284%29%2Bf%284%29g%284%29%5D%3D45..........%28i%29)
Now applying the given value of g(4) in equation 'i' we get

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