1. Let it be known thatlimx→1f(x)=2,limx→10f(x)=1,f(1)=5;limx→1g(x)=1,limx→10g(x)=101,g(1)=1.Find the limits of the functions if possible. If the boundary cannot be determined, explain why.1) limx→1f2(x)2f(x)+g(x);2) limg());3) limx→1f(2g(x));4) limx→10lg(g(x));5) limx→105f(x).2. Find limx→3f(x) if 6x−9≤f(x)≤x2. Explain the answer.
Q. 1. Let it be known thatlimx→1f(x)=2,limx→10f(x)=1,f(1)=5;limx→1g(x)=1,limx→10g(x)=101,g(1)=1.Find the limits of the functions if possible. If the boundary cannot be determined, explain why.1) limx→1f2(x)2f(x)+g(x);2) limg());3) limx→1f(2g(x));4) limx→10lg(g(x));5) limx→105f(x).2. Find limx→3f(x) if 6x−9≤f(x)≤x2. Explain the answer.
Given Limits Calculation: We're given limx→1f(x)=2 and f(1)=5. For the first limit, we need to plug in the values into the function f2(x)2f(x)+g(x). Since we know f(1) and g(1), we can substitute them in.
Calculation of First Limit: So, limx→1f2(x)2f(x)+g(x)=522⋅5+1=2510+1=2511.
Issue with Second Limit: Next, we look at limg(). This doesn't make sense because there's no limit point given. We can't solve this.