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Problem 35 Easy Difficulty

Use continuity to evaluate the limit.

$ \displaystyle \lim_{x \to 2} x \sqrt{20 - x^2} $

Answer

The number 2 is in that domain, so $f$ is continuous at $2,$ and $\lim _{x \rightarrow 2} f(x)=f(2)=2 \sqrt{16}=8$

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Video Transcript

This is problem thirty five Stewart Calculus, eighth edition, Section two point five. Use continuity to evaluate the limit. A limit, his expertise to X multiplied by the square root of the quantity twenty minus X squared Here to the rain to recall we have the definition of continuity. Um, that if a function of its continuous a point Okay, then the limit is expert Jesse. There was a function of is equal to f A A. If we look at this function, you see that it is eh? Combination. The product of two continuous functions we have am xs one function. The square root is another function. And then within its where we also have a polynomial which is continuous on its domain. And we have no domain restrictions, especially you. X equals a rex equals two. So because we know this function is continuous, the solution to this limit will be the the foot dysfunction evaluated it too. So two times the square root twenty minutes to squared, which is two times the square root of twenty minutes for or sixteen. Just two teams for we're just going to be eight, and that is our final answer.