This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MATH 221 —— THE SECOND MIDTERM November 7, 2007 Your TA: (circle one)
Zajj Daugherty Junwu Tu Rachel Davis Derek 'Garton (1) Compute the derivative of each of the following (Show your work). sinx , __ (a) we): Meow =: M)—
__ 1+3:2 dy_
(b)y 111(1_$c)2 =¢ El;— (c) ﬂit) == v 1+6” ==>> NIB) _ ((1) Find the 10th derivative of f 2 62¢ — 6"”2. (2) The function y = f satisﬁes
all + y = say/2 for all x.
(a) For which value of ac does one have y = 2? ﬂy. (b) Compute d3: When y = 1. (3) An extending ladder is placed against a wall. The angle it
makes with the floor is 0 and its length is L. The bottom
of the ladder is anchored at a point which is 12 feet away
from the wall. When the ladder is 15 feet long, its length is decreasing by
0.5ft/sec. What is the rate of change of the angle 6 at that
moment? L( t) 12ft (4) Consider the function f = \/_ — {1/5
' (a) Find the interva1(s) on which f is increasing. Find the local maxima and minima
of f on the interval 0 < a: < oo. _ (b) Find the intervals on which f is convex or concave. Find the inﬂection point(s)
in the graph of f. (5) Find the largest value and the smallest value which the functioﬁ v f(:z:) = arcsin(a:) + 2V1 4— 252 can have on the (closed) interval 0 S a: g 1. ...
View
Full Document
 Summer '07
 Denissou
 Calculus, Geometry, Derivative, Mathematical analysis, Convex function, Daugherty Junwu Tu

Click to edit the document details