Let the function f: R→ R be defined by f(x) = { Question 1 0, x2, x=0, x = 0. (a) Explain the differentiability of f on R by using definition.
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- Assume that f: R→ R and g: R → R are infinitely differentiable functions. Prove the following generalization of the product rule: dn dxn n (f(z)g(2)) - (1) (M) (2) g-) (x)}) = k=0Give one problem for partial differentiation of function of U with respect to 3 independent variables x, y, and z and solve ???zUse Green's Thoerem to evaluate F- dr. where F(2, y) = (-3/x² + 2, 7 tan '(x)) and C is the triangle from (0, 0) to (2, 2) to (0, 2) to (0, 0).
- Verify whether the function f(z) = e^x (cos y + isin y) satisfies Cauchy-Riemann equations or not.Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) = f** g'(x) = 5 5 x + 1 5 ³+5 dt Enhanced Feedback Please try again. Recall the Fundamental Theorem of Calculus: If f is differentiable on [a, b], then the function g defined by g(x) = = √² f(t)dt, a ≤ x ≤ b, is continuous on [a, b] and differentiable on (a, b), and g'(x) = f(x).what is f'of x