2. Consider the problem u"(x) + u'(x) = f(x) u'(0) = u(0) = [u'(1) + u(1)], with f(x) a given function. (a) Is the solution unique? Explain. (b) Does a solution necessarily exist, or is there a condition that f(x) must satisfy for existence? Explain.

I need the answer as soon as possible

2. Consider the function f (x, y) = x² + y² - 4 X - - 1 (a) Find and sketch the domain of f (x, y). (b) Give two points, as ordered pairs, that are not in the domain of this function.

Consider the following functions. f,(x) = 2 + x, f,(x) = x, f;(x) = x² g(x) = cf,(x) + cf2(x) + czf3(x) Solve for c,, Ca, and c, so that g(x) = 0 on the interval (-, o). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution (0, 0, 0}.) {c,, c2, c3} = Determine whether f,, fa, f, are linearly independent on the interval (-, ). o linearly dependent linearly independent

Let f(x) = -x-1, h(x) = -x + 5. Find (h of)(2). -0 (hof)(2) =

Q.1 Choose the correct one. () Domain of a function f(x) = V4-x i .. ......... (a) (-,4] (b) all real numbers (c) (4,) (d) (4,0] (1I) A function f(x) = x'+x' is... (a) Even (b) odd (c) none (d) neither even nor odd (I) Absolute value of any real number is always... (a) Positive (b) negative (c) both (d) even (IV) A polynomial function of degree one is called.. (a) Constant function (b) linear function (c) Quadratic function (d) none of these (V) If f(x) = 5x' +x + 4, then f(-2)=-- (a) 48 (b) 48 (c) 32 (d) none of these

Please help with part b)

2.(23) let g(v)