(i) (5 marks) Let F(x, y, z) = (sin(y), x cos(y) + cos(z), -ysin (z)). Let...

 

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(i) (5 marks) Let F(x, y, z) = (sin(y), x cos(y) + cos(z), -ysin (z)). Let C be the curve given by Y130 CUHK Examination ENGGH130 CUHK Examination ENGGI130 CUIK Examin CG1130 CUHK Examination ANGG130 CH Famination ENGG1130 CUHK Examin G1130 CUHK Examination r(t) = (sin t, t, 2t) for 0 ≤ t ≤ 2. ENGGI130 CUHK Examin ENGGIL30 CUHK Examination Is F conservative? Explain your answer clearly. IK Examination ENGGH130 CUHK Examination ENGGI130 CUHK Examination ENGGH130 CUHK Examination ENGGH130 CUHK Examination ENGGH130 CULIK Examination ENGGI130 CUHK Examination ENGGI130 CULIK Examination ENGGI130 CUHK Examination ENGGH130 CUHK Examination ENGGI130 CUHK Examination ENGGH130 CUHK Examination ENGGI130 CUHK Examination ENGGI130 CUHK Examination ENGGI130 CUHK Examination ENGGH130 CUHK Examination (ii) (5 marks) Given a line integral GG1130 CUHK Examination GG1130 CUHK Examination GI130 CUHK Examination SGH130 CUHK Examination G1130 CULIK Examination GI130 CUHK Examination where k is a real number.com SG1130 CUHK Examination Find the possible value(s) of k between any two given points. SGU30 CULIK Examination ENGGH30 CUHK Examin ENGG1130 CUHK Examin ENGGI130 CUHK Examin ENGG1130 CUHK Examin ENGGI130 CUIK Examin ENGGH130 CUHK Examin ENGGH130 CUHK Examin ENGGI130 CULIK Examin ENGGH130 CUHK Examin ENGGI130 CUHK Examin ENGGH30 CUHK Examin ENGGI130 CUHK Examin ENGGI130 CUHK Examin ENGG1130 CUHK Examin ENGGI130 CUIK Examin ENGGH130 CUHK Examin ENGGH130 CUHK Examin ENGGI130 CULIK Examin ENGGH130 CUHK Examin ENGGI130 CULIK Examination ENGG1130 CUBIC Exy3ion ENGGI130 CUHK Examin [kzy³dx+xzy²dy+dz ENGG130 CULIK Exami NGGI130 CULIK Exansnation ENGGI130 CUHK Examination ENGG1130 CUHK Examination ENGGH130 CUHK Examination such that the line integral is independent of the path, C, taken mi ENGG1130 CULIK Examination ENGGH130 CUHK Examin ENGGH130 CUHK Examination ENGGI130 CULIK Examin ENGG1130 CUHK Examin ENGGI130 CUHK Examin ENGG1130 CUHK Examin ENGGI130 CUIIK Examin GI130 CUHK Examination G1130 CUHK Examination SG1130 CUHK Examination G1130 CUHK Examination SG1130 CUHK Examination SGH130 CUHK Examination G1130 CUHK Examination G1130 CUHK Examination SGH130 CUHK Examination G1130 CUIK Examination GH130 CUHK Examination G1130 CUHK Examination GH130 CUHK Examination G1130 CUHK Examination с (i) (5 marks) Let F(x, y, z) = (sin(y), x cos(y) + cos(z), -ysin (z)). Let C be the curve given by Y130 CUHK Examination ENGGH130 CUHK Examination ENGGI130 CUIK Examin CG1130 CUHK Examination ANGG130 CH Famination ENGG1130 CUHK Examin G1130 CUHK Examination r(t) = (sin t, t, 2t) for 0 ≤ t ≤ 2. ENGGI130 CUHK Examin ENGGIL30 CUHK Examination Is F conservative? Explain your answer clearly. IK Examination ENGGH130 CUHK Examination ENGGI130 CUHK Examination ENGGH130 CUHK Examination ENGGH130 CUHK Examination ENGGH130 CULIK Examination ENGGI130 CUHK Examination ENGGI130 CULIK Examination ENGGI130 CUHK Examination ENGGH130 CUHK Examination ENGGI130 CUHK Examination ENGGH130 CUHK Examination ENGGI130 CUHK Examination ENGGI130 CUHK Examination ENGGI130 CUHK Examination ENGGH130 CUHK Examination (ii) (5 marks) Given a line integral GG1130 CUHK Examination GG1130 CUHK Examination GI130 CUHK Examination SGH130 CUHK Examination G1130 CULIK Examination GI130 CUHK Examination where k is a real number.com SG1130 CUHK Examination Find the possible value(s) of k between any two given points. SGU30 CULIK Examination ENGGH30 CUHK Examin ENGG1130 CUHK Examin ENGGI130 CUHK Examin ENGG1130 CUHK Examin ENGGI130 CUIK Examin ENGGH130 CUHK Examin ENGGH130 CUHK Examin ENGGI130 CULIK Examin ENGGH130 CUHK Examin ENGGI130 CUHK Examin ENGGH30 CUHK Examin ENGGI130 CUHK Examin ENGGI130 CUHK Examin ENGG1130 CUHK Examin ENGGI130 CUIK Examin ENGGH130 CUHK Examin ENGGH130 CUHK Examin ENGGI130 CULIK Examin ENGGH130 CUHK Examin ENGGI130 CULIK Examination ENGG1130 CUBIC Exy3ion ENGGI130 CUHK Examin [kzy³dx+xzy²dy+dz ENGG130 CULIK Exami NGGI130 CULIK Exansnation ENGGI130 CUHK Examination ENGG1130 CUHK Examination ENGGH130 CUHK Examination such that the line integral is independent of the path, C, taken mi ENGG1130 CULIK Examination ENGGH130 CUHK Examin ENGGH130 CUHK Examination ENGGI130 CULIK Examin ENGG1130 CUHK Examin ENGGI130 CUHK Examin ENGG1130 CUHK Examin ENGGI130 CUIIK Examin GI130 CUHK Examination G1130 CUHK Examination SG1130 CUHK Examination G1130 CUHK Examination SG1130 CUHK Examination SGH130 CUHK Examination G1130 CUHK Examination G1130 CUHK Examination SGH130 CUHK Examination G1130 CUIK Examination GH130 CUHK Examination G1130 CUHK Examination GH130 CUHK Examination G1130 CUHK Examination с

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i To determine if the vector field Fx y z siny x cosy cosz ysinz is conservative we need to check if it satisfies the condition of being a gradient fi... View the full answer