Consider the limit: lim x→0csc(6x)sin(7x).(a) What is the form of the limit?(b) Based on the form, what is the range of possible values the limit can take?(c) You can’t apply L’Hopital’s rule in its current form. Why not? (Hint: L’Hopital’s rule is a theorem...)(d) Manipulate the limit without changing the result so that you can apply L’Hopital’s rule. Explain why, after this manipulation, you can apply L’Hopital’s rule now.(e) Apply L’Hopital’s rule and determine the result of this limit. Verify that the result is within the range you provided in part (b).

Question

Consider the limit: lim x→0
csc(6x)sin(7x).
(a) What is the form of the limit?
(b) Based on the form, what is the range of possible values the limit can take?
(c) You can’t apply L’Hopital’s rule in its current form. Why not? (Hint: L’Hopital’s rule is a theorem...)
(d) Manipulate the limit without changing the result so that you can apply L’Hopital’s rule. Explain why, after this manipulation, you can apply L’Hopital’s rule now.
(e) Apply L’Hopital’s rule and determine the result of this limit. Verify that the result is within the range you provided in part (b).

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Limits

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