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find the horizontal and vertical tangents to
x
=
cos
(
3
t
)
and
y
=
2
sin
(
t
)
?
. Find the limits lim (𝑥,𝑦)→(2,−4) 𝑦+4 𝑥 2𝑦−𝑥𝑦+4𝑥 2−4�
Use eigen function expansions to find for value problem. Note: Differential equation must be satisfied 0<x<1, t>0; the pairs of boundary conditions holds for t>0; and the initial conditions holds on 0<x<1.
ut=uxx+e-t , ux(0, t)=0, ux(1, t)+u(1, t)=0, u(x, 0)=1-x.
y Q = 300√ L − 4L, where Q denotes output and L denotes the size of workfor e, al ulate the value of marginal produ t of labour if L = 9
Solve the boundary value problem
y''+2y= −x
y(0)=0, y(1)+y'(1)=0
u cos y sinh x, sin y cosh x satisfy laplace equation?
Evaluate the integral, I (4x 2y) dxdy 3 in the region R bounded by x 0, x 2, y x and y x 2 .
Trace the curve x = (y – 1) (y – 2) (y – 5)
Questions 4 and 5 are based on the following information: The daily rate of sales of a product (in units per day) is approximated by the exponential function
S(t) = 1800 + 1500e−0,3t+1,5
with t the number of days it has been on the market.
Question 4
After 20 days the rate of sales of the product is approximately
1. 37.
2. 108.
3. 1 817.
4. 1 783.
Question 5
After how many days, rounded to a whole number, will the rate of sale be 2 000 units per day?
1. 4
2. 5
3. 11
4. 12
