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Question 62 asks you to find a limit graphically and then use the standard theorem to confirm your answer.
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So we're trying to find a limit of x squared of cosine 1 divided by x squared as x approaches 0.
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The green graph right here is our function that we're trying to find the limit of.
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And as you can see, as x approaches 0 from the right, and as x approaches 0 from the left, it approaches 0.
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So graphically we can see that the limit approaches 0.
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So now let's use sandra's theorem in order to confirm our answer.
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So standard theorem states that, you know, if we can't find a limit directly, we can find it indirectly.
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So if a function is sandwiched in between two functions, we can use the limits of the, you know, the two graphs that is sandwiched in between of in order to find our limit.
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So this blue graph right here, this blue function, is y equals x squared.
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This red function right here is y equals negative x squared.
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So keep that in mind as we are going to use a standard theorem to confirm it algebraically.
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So we know that the bounds of a cosine graph is from negative 1 to positive 1...