Barrons AP Calculus - David Bock
(C) In the figure, the curve for y = ex has been superimposed on the slope field. ...
(C) The general solution is y = 3 ln|x^2 − 4| + C. The differential equation reveals that the derivative does not exist for x = ...
(A) The solution curve shown is y = ln x, so the differential equation is ...
(D) = sec θ; dx = sec^2 θ; 0 ≤ x ≤ 1; so 0 ≤ θ ≤ ...
(C) The equations may be rewritten as = sin u and y = 1 − 2 sin^2 u, giving ...
(D) Use the formula for area in polar coordinates, then the required area is given by (See polar graph 63 in the Appendix.) ...
44. (C) ...
(A) The first three derivatives of The first four terms of the Maclaurin series (about x = 0) are 1, + 2x, Note also that repr ...
(D) We use parts, first letting u = x^2 , dv = e−x dx; then du = 2x dx, v = −e−x and Now we use parts again, letting u = x, dv ...
(E) Use formula (20) in the Appendix to rewrite the integral as ...
(E) The area, A, is represented by ...
49. (D) ...
(C) Check to verify that each of the other improper integrals converges. ...
(D) Note that the integral is improper. See Example 26. ...
(C) Let Then ln y = −x ln x and Now apply L’Hôpital’s Rule: So, if ln y = 0, then ...
(D) The speed, |v|, equals and since x = 3y − y^2 , Then |v| is evaluated, using y = 1, and equals ...
(A) This is an indeterminate form of type use L’Hôpital’s Rule: ...
(E) We find A and B such that After multiplying by the common denominator, we have 3 x + 2 = A(x − 4) + B(x + 3). Substituting ...
(B) Since Then Note that so the integral is proper. ...
(D) We represent the spiral as P(θ) = (θ cos θ, θ sin θ). So ...
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