Find the following limits proving whether they exist or do not exist 5y¹ cos²x x² + y² C) D) lim (x,y) → (0,0) x² sin² y lim (x,y) → (0,0) x² + 2y²
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A: Ans=(d) 0.57 For detail go through the solution I have solved step by step in detail
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- A function h(x, y) is defined by h(x,y)=(x^2 y)/(〖7x〗^6+y^3 ). Verify the limit over h(x, y) exists at the origin along y = x^2? In either case write also the reason.By writing the ODEs in their normal form near the bifurcation point show that (a) ˙x = 1 + rx x cos(x) + sin(r) undergoes a saddle-node bifurcation at (r∗ , x∗ ) = (0, 0), (b) ˙x = (r2 2 r + 1)(x + x3) ) ln(1 + x) undergoes a transcritical bifurcation at (r∗ , x∗ ) = (1, 0). Please specify the order of the approximation as an error in ε > 0 and the corresponding size of r, x, e.g. |x - x∗| < ε.Evaluate the limit (b) limt→0 < sin(t)/t,(1−cos(t))/t,−2t/t)>
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