I have to find $\lambda$ so that the function:
has a limit at $x0=2$. I've tried to write the limit of 2x + $\lambda$ as $x \to -\infty$ equals to 2. But I have no idea what to do with $x^2+1$. Please help me solve this...
I am not sure, but I suspect that it is about a limit in $0$ here. Function $f$ has a limit at $0$ if $\lim_{x\downarrow0}f\left(x\right)$ and $\lim_{x\uparrow0}f\left(x\right)$ both exist and are equal. It is clear that $\lim_{x\downarrow0}f\left(x\right)=f\left(0\right)=1$. You have $\lim_{x\uparrow0}f\left(x\right)=\lambda$. So $f$ has a limit at $0$ if $\lambda=1$. Only in this context I can understand the exercise.
x \to -\infty
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