Question

Calculate differentiability of f(x,y,z) = x^2 + y^2 + z^2 this function is defined in R^2

Calculate differentiability of f(x,y,z) = x^2 + y^2 + z^2

this function is defined in R^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
Consider the function f defined on R by f(x) = ?0 if x ≤ 0, f(x)...
Consider the function f defined on R by f(x) = ?0 if x ≤ 0, f(x) = e^(−1/x^2) if x > 0. Prove that f is indefinitely differentiable on R, and that f(n)(0) = 0 for all n ≥ 1. Conclude that f does not have a converging power series expansion En=0 to ∞[an*x^n] for x near the origin. [Note: This problem illustrates an enormous difference between the notions of real-differentiability and complex-differentiability.]
] Consider the function f : R 2 → R defined by f(x, y) = x...
] Consider the function f : R 2 → R defined by f(x, y) = x ln(x + 2y). (a) Find the gradient of f(x, y) at the point P(e/3, e/3). (b) Use the gradient to find the directional derivative of f at P(e/3, e/3) in the direction of the vector ~u = h−4, 3i. (c) Find a unit vector (based at P) pointing in the direction in which f increases most rapidly at P.
Consider the function f : R 2 → R defined by f(x, y) = 4 +...
Consider the function f : R 2 → R defined by f(x, y) = 4 + x 3 + y 3 − 3xy. (a)Compute the directional derivative of f at the point (a, b) = ( 1 2 , 1 2 ), in the direction u = ( √ 1 2 , − √ 1 2 ). At the point ( 1 2 , 1 2 ), is u the direction of steepest ascent, steepest descent, or neither? Justify your...
s] Consider the function f : R 2 → R defined by f(x, y) = x...
s] Consider the function f : R 2 → R defined by f(x, y) = x ln(x + 2y). (a) Find the gradient of f(x, y) at the point P(e/3, e/3). (b) Use the gradient to find the directional derivative of f at P(e/3, e/3) in the direction of the vector ~u = h−4, 3i. (c) Find a unit vector (based at P) pointing in the direction in which f increases most rapidly at P.
Consider the function f : Z → Z defined by f(x) = x 2 . Is...
Consider the function f : Z → Z defined by f(x) = x 2 . Is this function one-to-one, onto, or neither? Give justification for your claims that rely on definitions. With explanation please
Let f(x, y) = x^3 − 4xy^2 , x, y ∈ R. Use the definition of...
Let f(x, y) = x^3 − 4xy^2 , x, y ∈ R. Use the definition of differentiability to show that f(x, y) is differentiable at (2, 1).
1. A function f : Z → Z is defined by f(n) = 3n − 9....
1. A function f : Z → Z is defined by f(n) = 3n − 9. (a) Determine f(C), where C is the set of odd integers. (b) Determine f^−1 (D), where D = {6k : k ∈ Z}. 2. Two functions f : Z → Z and g : Z → Z are defined by f(n) = 2n^ 2+1 and g(n) = 1 − 2n. Find a formula for the function f ◦ g. 3. A function f :...
Evaluate the double integral for the function f(x, y) and the given region R. f(x, y)...
Evaluate the double integral for the function f(x, y) and the given region R. f(x, y) = 5y + 5x; R is the rectangle defined by 5 ≤ x ≤ 6 and 2 ≤ y ≤ 4
The average value of a function f(x, y, z) over a solid region E is defined...
The average value of a function f(x, y, z) over a solid region E is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the volume of E. For instance, if ρ is a density function, then ρave is the average density of E. Find the average value of the function f(x, y, z) = 5x2z + 5y2z over the region enclosed by the paraboloid z = 4 − x2 − y2 and the...
Is the function f : R → R defined by f(x) = x 3 − x...
Is the function f : R → R defined by f(x) = x 3 − x injective, surjective, bijective or none of these? Thank you!
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT