Question

Find the derivative of w=4ck^2q. Assume c and k are constants.

Answer #1

Let f = sin(yz) + ln(x)
a) Find the derivative of F at P(1,1,Pi) in the direction of v =
i+j-k
b) Find a vector u in the direction where f increases the
fastest
c) Find a nonzero vector w with the property that the derivative
of f in the direction of w at P(1,1,pi) is 0

Find the derivative of each of the following functions:
(a) y=x^12 (c) y=7x^5 (e) w=-4u^(1/2)
(b) y =63 (d) w=3u^(-1) (f) w=4u^(1/4)
2. Find the following:
(a) d/dx(-x^(-4)) (c) d/dw 5w^4 (e) d/du au^b
(b) d/dx 9x^(1/3) (d) d/dx cx^2 (f) d/du-au^(-b)
3. Find f? (1) and f? (2) from the following functions: Find the
derivative of each of the following functions:
(c) y=x^12 (c) y=7x^5 (e) w=-4u^(1/2)
(d) y =63 (d)w=3u^(-1) (f) w=4u^(1/4)
4.
(a) y=f(x)=18x (c) f(x)=-5x^(-2)...

Show that x(t) = A sin(wt) sin(kx) satisfies the wave equation,
where w and k are some constants. Find the relation between w, k,
and v so that the wave equation is satisfied.

Find the value of the directional
derivative of the function w = f ( x , y , z ) = 2 x y + 3 y z
- 4 x z
in the direction of the vector v =
< 1 , -1 , 1 > at the point P ( 1 , 1 , 1 ) .

Rate constants for the reaction A → B + C are 1.55 s-1 at 298 K
and 17.2 s-1 at 308 K.
A. What is the activation energy (Ea) for this reaction?
B. What would the rate constant be at 318 K?
C. What is the order of this reaction?

LB = {w|w e {a,b,c}^*, w =c^kbba^n, n<k}.
1. Is LB regular or not?
2. Give proof that supports your answer.

q(L,K)=2LK=100; w=25; v=50; TC=500
i. find the cost-minimizing input combinations (L*,K*)
ii Based on part i grapg this cost minimization case
iii. Now assume that w=30 and v=50. explain what happens to our
isocost and (L*,K*)
iv. Assume that w=25; v=50 repeat parts i and ii
a. q(L,K)=2L+K=100
b. q(L,K)=min(2L,K)=100

Find the 4th moment (Find the 4th derivative, then plug in
zero).
a) e ^ ( k ( e ^ t -1) )
b) a/ (a-t)
c) (a/ (a-t)) ^ r
d) e ^ ( (1/2) t ^2)

For a firm with production function f(L,K)=√L+√K, find its cost
function for arbitrary values of w and r. That is,find a formula
for the cost of producing q units that includes q,and also w and
r,as variables. Also find marginal and average cost,and draw a plot
that shows both cost functions in the same graph.

For a firm with production function f(L,K)=√L+√K, find its cost
function for arbitrary values of w and r. That is,find a formula
for the cost of producing q units that includes q,and also w and
r,as variables. Also find marginal and average cost,and draw a plot
that shows both cost functions in the same graph.

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