Q1) The arc length L of the curve C: r(t) = 3 cos(t)i + 3 sin(t))+...

 

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Q1) The arc length L of the curve C: r(t) = 3 cos(t)i + 3 sin(t))+ 4tk from t= 0 tot mis a) L = n/2 b) 10m c) L = 5m d) Sm/2 dz Q2) If e* sin(y) = xz²+ xy²-4, then at (1 0.2) is b) c)-1 Q3) If f(x y) = e cos(xy)In(x² + y²)+5y + 4x + 10, then f, (0:1) = a) 5 b) 4 c) 6 d) 7 Q4) The maximum directional derivative of the f(x,y,z) == at (8 3,1 ) is y+2 b c) 9 16 Q5) The graph on the right represents the domain of the function a) f(x,y)=√√y² + x²-4 b) f(x y) = √4-y²-x² c) f(x, y) = In(y² +x²-4) d) f(x, y) = In (4-y² – x²) Q6) The direction vector for the tangent line to the curve Cr(t) = (t.t² 2t) at t = -1 is a) 1-2j-2k b) i +2j+2k c) i-2j + 2k d)i-2j-2k Q1) The arc length L of the curve C: r(t) = 3 cos(t)i + 3 sin(t))+ 4tk from t= 0 tot mis a) L = n/2 b) 10m c) L = 5m d) Sm/2 dz Q2) If e* sin(y) = xz²+ xy²-4, then at (1 0.2) is b) c)-1 Q3) If f(x y) = e cos(xy)In(x² + y²)+5y + 4x + 10, then f, (0:1) = a) 5 b) 4 c) 6 d) 7 Q4) The maximum directional derivative of the f(x,y,z) == at (8 3,1 ) is y+2 b c) 9 16 Q5) The graph on the right represents the domain of the function a) f(x,y)=√√y² + x²-4 b) f(x y) = √4-y²-x² c) f(x, y) = In(y² +x²-4) d) f(x, y) = In (4-y² – x²) Q6) The direction vector for the tangent line to the curve Cr(t) = (t.t² 2t) at t = -1 is a) 1-2j-2k b) i +2j+2k c) i-2j + 2k d)i-2j-2k