Quiz 7-3 to 7-5 Trig Integrals Trig Substitution (notecard)

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Quiz 7-3 to 7-5 Trig Integrals Trig Substitution (notecard) Partial Fractions

True/False 1) A limit describes how a function moves as x moves toward a certain point. 2) A limit is a number or point past which a function cannot go. 3) A limit is a number that the y-values of a function can be made arbitrarily close to by restricting x-values.

True/False 4) A limit is a number or point the functions gets close to but never reaches. 5) A limit is an approximation that can be made as accurate as you wish. 6) A limit is the value reached by plugging in numbers closer and closer to a given number.

Indeterminate Forms and L’Hopital’s Rule Section 7.7 AP Calc

Find the limit:

Thm 7.3 Extended Mean Value Theorem If f and g are differentiable on an open interval (a,b) and continuous on [a,b] such that g’(x)≠0 for any x in (a,b), then there exists a point c in (a,b) such that

Thm 7.4 L’Hopital’s Rule Let f and g be functions that are differentiable on an open interval (a,b) containing c, except possibly at c itself. Assume g’(x)≠0 for all x in (a,b), except possibly at c itself. If the limit of f(x)/g(x) as x approaches c produces the indeterminate form 0/0, then

provided the limit on the right exists (or is infinite) provided the limit on the right exists (or is infinite). This result also applies if the limit of f(x)/g(x) as a approaches c produces any one of the indeterminate forms ∞/∞, (- ∞)/ ∞, ∞/(- ∞), or (- ∞)/(- ∞).

Determine the limits: A) B)

C) D)

Other indeterminate forms:

Find the limit: E)

F) G)

Use Graphing Calculator to check limits Notice: