MATH 140B - HW 1 SOLUTIONS Problem1(WR Ch 5 #6). Suppose (a) f is continuous for x ‚0, (b) f 0 (x) exists for x ¨0, (c) f (0) ˘0, (d) f 0 is **monotonically** increasing,

Since we specified the power used to create a **monotonically** increasing or decreasing function, we knew that the power transformation to reverse the effect of the power would be its inverse.

I could take the natural logarithm ofu (x) above, which isa **monotonically** increasing transformation, to get U (x) =a 1 lnx 1 +a 2 lnx 2 + a n lnx n Forgiven a 1;a 2;:::;a n, the functionsu (x) and U (x) represent exactly the same preferences.

The Maclaurinseries for e ¡ ( -=x ) is e ¡ ( -=x ) =1 ¡-x + 1 2-2 x 2 ¡ 1 3!-3 x 3 + ¢¢¢: Since-x < 1, the Maclaurin series above has absolutely **monotonically** decreasing, alternating terms and so e ¡ ( -=x ) > 1 ¡-x.

Let * () Pqbe a peak price in the system in the event of withholding all capacity above the level q: * (() ) () SPqqDTp δ δ += − and therefore * () Pqis a **monotonically** non-descending function of q.

The algorithm generatesa sequence of all subsets of a set of n elements in which the number of elements in each subset is **monotonically** increasing.

This paper consists of as follows: In Section II, a briefexpla-nation about the super-vector ILC is given and in Section III, the **monotonically** convergent ILC system is designed with Corresponding author: Prof. Ya ngQuan Chen, Center for Self-Organizing and Intelligent Systems, Dept. of Electrical and ...

Show that P [ X = k ]increases **monotonically** and then decreases **monotonically** as k increases, reaching its maximum value when k is the largest integer not exceeding fi .

Drift at failure for cyclically tested walls occurred closer to drift at capacity than **monotonically** tested walls, resulting in load resistance at failure to be a higher percentage of capacity than **monotonically** tested walls.

This is important because, in reality, short cracks can behave quite differently from larger cracks, in particular by exhibiting rising fracture resistance with extension under **monotonically** increasing loading, i.e., R -curve behavior. 4-12 Although R -curve behavior has been extensively studied in ...