Calculus Answers

Let f : R²→R,f(x,y) =2xy/x²+y² When (x,y) ≠(0,0) and f(x,y) =0, otherwise. How to Check whether or not f has a directional derivative at (0, 0) in the direction θ=π/4? Deduce that the function f is not differentiable at the point (0, 0)?

Suppose that a certain market supplies x thousands of crates of orange daily when p dollars is the price per crate, and the supply equation is px-20p-3x+105=0. If the daily supply decreases at the rate of 250 crates per day, at what rate is the price changing when the daily supply is 5000 crates? 

The demand equation for a particular kind of shirt is 2px+65p-4950=0, where x hundreds of shirts are demanded per week when dollars is the price of a shirt. Suppose that the shirt is selling this week at $30, and the price increases at the rate of $0.20 per week. Find the rate of change in demand. 

A piece of wire 20 m long is cut into two pieces. One piece is bent into a square and the

other is bent into an equilateral triangle. How should the wire be cut so that the total area

enclosed is:

(a) maximum? (b) minimum?

find workdone integral of F



d

~

r

where

~

F

(

x

,

y

,

z

)

=

e

2

x

~

i

+

z

(

y

+

1

)

~

j

+

z

3

~

k

along the curve

C

~

r

(

t

)

=

t

3

~

i

+

(

1

−

3

t

)

~

j

+

e

t

~

k

for 0

≤

t

≤

2

Calculate the approximate value of √26 to four decimal places using Taylor series method.

4.Expand log (cosx) about the point.

Find the directional derivative of f (x, y,z) = x2y3 − 4xz in the direction of f (x, y,z) = x2y3 − 4xz