Question

1.Show that near the origin,sinx+siny≈x+y 2.Find the first order partial derivatives of f (x, y, z)...

1.Show that near the origin,sinx+siny≈x+y

2.Find the first order partial derivatives of
f (x, y, z) = xysin (xy) + e^z^2

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
show that f: R^2->R^2 be f(x,y)= (cosx + cosy, sinx + siny). show that f is...
show that f: R^2->R^2 be f(x,y)= (cosx + cosy, sinx + siny). show that f is locally invertible near all points (a,b)such that a-bis not = kpi where k in z and all other points have no local inverse exists  
Find the first- and second-order partial derivatives for the following function. z = f (x, y)...
Find the first- and second-order partial derivatives for the following function. z = f (x, y) = (ex +1)ln y.
2. (a) Determine all first and second order partial derivatives of f(x,y,z) = x2y3 sin(xz) (b)...
2. (a) Determine all first and second order partial derivatives of f(x,y,z) = x2y3 sin(xz) (b) Determine all first-order partial derivatives of g(x,y,z)=u2y+x2v where u=exz, v=sin(yz)
part 1) Find the partial derivatives of the function f(x,y)=xsin(7x^6y): fx(x,y)= fy(x,y)= part 2) Find the...
part 1) Find the partial derivatives of the function f(x,y)=xsin(7x^6y): fx(x,y)= fy(x,y)= part 2) Find the partial derivatives of the function f(x,y)=x^6y^6/x^2+y^2 fx(x,y)= fy(x,y)= part 3) Find all first- and second-order partial derivatives of the function f(x,y)=2x^2y^2−2x^2+5y fx(x,y)= fy(x,y)= fxx(x,y)= fxy(x,y)= fyy(x,y)= part 4) Find all first- and second-order partial derivatives of the function f(x,y)=9ye^(3x) fx(x,y)= fy(x,y)= fxx(x,y)= fxy(x,y)= fyy(x,y)= part 5) For the function given below, find the numbers (x,y) such that fx(x,y)=0 and fy(x,y)=0 f(x,y)=6x^2+23y^2+23xy+4x−2 Answer: x= and...
find the first partial derivatives of f(x,y) = ln(x^2+2xy+x^2+1)
find the first partial derivatives of f(x,y) = ln(x^2+2xy+x^2+1)
a. Is F(x,y,z)= <(e^z)siny,(e^z)cosx,(e^x)siny> a conservative vector field? Justify. b. Is F incompressible? Explain. Is it...
a. Is F(x,y,z)= <(e^z)siny,(e^z)cosx,(e^x)siny> a conservative vector field? Justify. b. Is F incompressible? Explain. Is it irrotational? Explain. c. The vector field F(x,y,z)= < 6xy^2+e^z, 6yx^2 +zcos(y),sin(y)xe^z > is conservative. Find the potential function f. That is, the function f such that ▽f=F. Use a process.
(1 point) Find all the first and second order partial derivatives of f(x,y)=7sin(2x+y)−2cos(x−y) A. ∂f∂x=fx=∂f∂x=fx= B....
(1 point) Find all the first and second order partial derivatives of f(x,y)=7sin(2x+y)−2cos(x−y) A. ∂f∂x=fx=∂f∂x=fx= B. ∂f∂y=fy=∂f∂y=fy= C. ∂2f∂x2=fxx=∂2f∂x2=fxx= D. ∂2f∂y2=fyy=∂2f∂y2=fyy= E. ∂2f∂x∂y=fyx=∂2f∂x∂y=fyx= F. ∂2f∂y∂x=fxy=∂2f∂y∂x=fxy=
Find the four second partial derivatives of f(x, y) = 2x^5y^2 + x^2 y. please show...
Find the four second partial derivatives of f(x, y) = 2x^5y^2 + x^2 y. please show all work
Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y),...
Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y), where x = r2 + s2 and y = 6rs, find ∂2z/∂r∂s. (Compare with Example 7.) ∂2z/∂r∂s = ∂2z/∂x2 + ∂2z/∂y2 + ∂2z/∂x∂y + ∂z/∂y
1. f(x, y, z) = 2x-1 − 3xyz2 + 2z/ x4 2. f(s, t) = e-bst...
1. f(x, y, z) = 2x-1 − 3xyz2 + 2z/ x4 2. f(s, t) = e-bst − a ln(s/t) {NOTE: it is -bst2 } Find the first and second order partial derivatives for question 1 and 2. 3. Let z = 4exy − 4/y and  x = 2t3 , y = 8/t Find dz/dt using the chain rule for question 3.