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Limits & Continuityhard
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A tank is filled by two pipes. Pipe A fills the tank at rate RA(x)=1xR_A(x) = \frac{1}{x}RA​(x)=x1​ pools/hr, and Pipe B fills it at rate RB(x)=1x+4R_B(x) = \frac{1}{x+4}RB​(x)=x+41​ pools/hr. The combined time to fill the tank is T(x)=x(x+4)2x+4T(x) = \frac{x(x+4)}{2x+4}T(x)=2x+4x(x+4)​. What is lim⁡x→∞T(x)\lim_{x \to \infty} T(x)limx→∞​T(x)?