1. Let |x| = (x12 + x22)1/2. Define functions g(x1, x2) = x1x2e|x|2 , x = (x1, x2) ∈ R2   gradient ∇g and the points x where ∇g(x) = 0.

Q: Prove that the linear function f(x) = ax+b is continuous.

A: To prove that the given linear function is continuous.

Q: - Given the functions f(x) = x² + 1and g(x) = 3 − x, determine an equation for the combined function…

A:

Q: Identify an inner function (call it g) of y = (5x + 4)3.Let u = g(x) and express the outer function…

A: y=(5x+4)3

Q: Give two distinct linear functions ƒ and g that satisfy ƒ'(x) = g'(x); that is, the lines have equal…

A: It is given that fx and gx two distinct function.

Q: + a3X3 f (x1, x2, x3) = sin(@1)x1 + a2 + a3X3 + a3x3 f (x1, x2, x3) = sin(x1)a1 +

A:

Q: Let u and v be the linear functions defined asu(x)=2x+3,v(u)=3x-2.Find the compositions u*v and v*u.…

A: For uov, we do u(v(x)), and for v o u, we do v(u(x)) .

Q: Consider the function f(x)=∫x04t5+4t4−t3+2t2−3t−5dt. Compute f′′(x)

A:

Q: 4. Examine if functions f(x)= x , f2 (x) = x², f;(x)=x² – 2x are linearly independent.

A:

Q: 4. Show that the function f: R → R defined by f(x) = x² - 3x + 1 is not one-to-one.

A: