Barrons AP Calculus - David Bock

Answers Explained (B) The limit as x → 2 is 0 ÷ 8. ...

(D) Use the Rational Function Theorem. The degrees of P(x) and Q(x) are the same. ...

(C) Remove the common factor x − 3 from numerator and denominator. ...

(A) The fraction equals 1 for all nonzero x. ...

(D) Note that ...

(B) Use the Rational Function Theorem. ...

(A) Use the Rational Function Theorem. ...

(E) Use the Rational Function Theorem. ...

(C) The fraction is equivalent to the denominator approaches ∞ ...

(D) Since therefore, as x → −∞ the fraction → +∞ ...

11. (D) ...

12. (B) ...

(B) Because the graph of y = tan x has vertical asymptotes at the graph of the inverse function y = arctan x has horizontal as ...

(C) Since (provided x ≠ 3), y can be defined to be equal to 2 at x = 3, removing the discontinuity at that point. ...

(B) Note that ...

(C) As x → 0, takes on varying finite values as it increases. Since the sine function repeats, oscillates, taking on, infinitel ...

(A) Note that, since both x = 2 and are vertical asymptotes. Also, is a horizontal asymptote. ...

(B) Use the Rational Function Theorem. ...

(B) Since |x| = x if x > 0 but equals −x if x < 0, while ...

(E) Note that x can be rewritten as and that, as x → ∞, ...