10.3
... Since all of the above limits exist and are finite, f cannot have a vertical asymptote at x = a. In order for f to have a vertical asymptote at x = a, at least one of the limits above must be an infinite limit, and f must be discontinuous at x = a. We know that polynomial functions are continuous fo ...
... Since all of the above limits exist and are finite, f cannot have a vertical asymptote at x = a. In order for f to have a vertical asymptote at x = a, at least one of the limits above must be an infinite limit, and f must be discontinuous at x = a. We know that polynomial functions are continuous fo ...
Math 171 Final Exam Review: Things to Know
... • Know the definition of a limit. • Recall that lim f (x) = L if and only if lim+ f (x) = lim− f (x) = L. x→a ...
... • Know the definition of a limit. • Recall that lim f (x) = L if and only if lim+ f (x) = lim− f (x) = L. x→a ...
Continuous functions( (الدوال المستمرة introduction The concept of
... The concept of continuous function is basic to much of mathematics .continuous functions on the real line appear in the first of any calculus book ,and continuous functions in the plane and in a space follow and far behind ,more general kinds of continuous functions arise as one goes further in math ...
... The concept of continuous function is basic to much of mathematics .continuous functions on the real line appear in the first of any calculus book ,and continuous functions in the plane and in a space follow and far behind ,more general kinds of continuous functions arise as one goes further in math ...
Script #13
... Corollary 13.17. (Homework) Open balls are open. Corollary 13.18. A set U ⊂ Rn is open if and only if for every a ∈ U , there exists r > 0 such that B(a, r) ⊂ U . Remark 13.19. If X ⊂ Rn , then X is also a topological space with the subspace topology. That is, A ⊂ X is open in X if there exists an o ...
... Corollary 13.17. (Homework) Open balls are open. Corollary 13.18. A set U ⊂ Rn is open if and only if for every a ∈ U , there exists r > 0 such that B(a, r) ⊂ U . Remark 13.19. If X ⊂ Rn , then X is also a topological space with the subspace topology. That is, A ⊂ X is open in X if there exists an o ...
Semester Review
... Draw the graphs of 3 different types of continuous functions that are not differentiable at x = 2. Note: This means one and only one of your functions can have a corner. (Hint: other than a corner, how else can the graph of a function not have a derivative at a point?) ...
... Draw the graphs of 3 different types of continuous functions that are not differentiable at x = 2. Note: This means one and only one of your functions can have a corner. (Hint: other than a corner, how else can the graph of a function not have a derivative at a point?) ...
Summer 2016 HW - APCalculus AB SummerReview_2016
... Solve by direct substitution whenever possible. If needed, rearrange the expression so that you can do direct substitution. ...
... Solve by direct substitution whenever possible. If needed, rearrange the expression so that you can do direct substitution. ...