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Problem 46 Easy Difficulty

(a) By graphing the function $ f(x) = (\tan 4x)/x $ and zooming in toward the point where the graph crosses the $ y $ -axis, estimate the value of $ \displaystyle \lim_{x \to 0}f(x) $.

(b) Check your answer in part (a) by evaluating $ f(x) $ for values of $ x $ that approach 0.

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Video Transcript

This is problem number forty six of the Stuart Calculus eighth edition Section two point two Partying By grabbing the function improve, X equals ten jina for X the Betamax and zooming in toward the point where the graph crosses the Y axis. I estimate the value of Element and six approaches zero of this function. F Riddick E graphing tool and plug in this function tender for X rex, and we zoom in very closely two x zero. We see that the function approaches for from the left, and it also purchase for from the right. And although dysfunction is undefined at X equals zero because that would make the denominator equal to zero, we see that the limit is definitely equal two four because the limit from the left equals limit from the right equals four Carpi take care. Answered party by evaluating F for values of X that approach zero. So we're going on or for Tara spreadsheet and we'LL see that we used a table of values in order for us to plant dysfunction and as we see approaching the function approaching X equals zero from the right kidding X values closer and closer. Zero. We see that the function approaches Thor closer and closer. And also this is true from the left. As we approach the arrow from the left, the function gets closer and closer for in this confirms our solution at the limit has experts. Zero of the function F is equal to four.