Find only the residues * cot z coth z Find the residue of F(z) = at z = 0. z3 Don't use any Al tool show ur answer in pe n and paper then take

no use of comp plz

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az Find at (2, -2, 1) if | a2 + y? + z2 = 6xz + 6yz + 21 = 5 2/5

4. Let H be a Hilbert space, YcHa subspace of H.

Find of 3xy – x³ = 5 at (1, 2)

Find three horizontal tangents  between [0,10]

. ^. 4 let f(x)=2x²-36x² + 20. Find the intervals where f is increasing. a) (-3,0) 0(3, ~) b) (-3,0) 0 (0,3) c) (-₁-3) 0 (0,3) d) (-0⁰0, -3) 0 (3₁ e) (0,3)0 (3,00)

The twice-differentiable function f is shown below on the domain (-9, 9). The graph of f has points of inflection at x = -2, x = 4, indicated by small green circles. What inferences can be made about the graphs of f, f', and f" on the interval (4, 6)? Graph of f 8. 7 4 3 -10 -9 -8 -7 -5 -4 -3 2 6. 8. -1 1 3 4 7 10 -1 --2 -3 -4 -5 -6 -7 -8 From the figure given above, it can be seen that the graph ofƒ on the interval (4, 6) is| and Based on these observations, it can be concluded that: On the interval (4,6), the graph of f' would be because f is On the interval (4, 6), the graph of f" would be because f is

For each situation, find degree of freedom (d. f .), numerator, denominator, tobtained, and area under the curve (AUC) beyond tcritical, and fill out the empty cells.