43.44.45.so apply L’Hôpital’s Rule. You get , which is still of
the form ; therefore, apply L’Hôpital’s Rule again. The
new limit is by substitution is (C) . Since v(5) = 0,
−v(0) = −π + 3; so v(0) = π − 3.(D)(C) Let y = (x^3 − 4x^2 + 8)ecos(x(^2) )
. The equation of the tangent at point
(2,y(2)) is y − y(2) = y′(2)(x − 2). Note that y(2) = 0. To find the y-
intercept, let x = 0 and solve for y: y = −2y′(2). A calculator yields y =
4.161.