Use Green's Thoerem to evaluate F dr. where F(r, y) = (-3Vx² + 2, 7 tan '(x)) and C is the triangle from (0, 0) to (2, 2) to (0, 2) to (0, 0).

Q: Find y SX a) y = 3 sin (x² + 5x - 3) y' = c) y = sin" (6x) y'= b) xE5X+2 d) y = In (2x) Y₁ = Y y' =

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Q: Find the equation of the tangent to y = e A) y=-x-1 OB) y = ex+1 C) y=x+1 O D) D) y = x + x at x =…

A: Find the equation of the tangent to y= esinx at x=0.

Q: Evaluate f, f,(1-2) L(-dy dx dz

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Q: Show that r' x r" is a multiple of B. Conclude that r' x r" B = ||r' x r"||

A: Given, B=r'×r"r'×r" we know cross product of two vector is always a vector. r'×r"=r→ magnitude of…

Q: Find dw/dr and dw/dΘ for w=2z/y-3x if x=3Θ+2r, y=3r^2 + Θ, and z =4r-Θ, where Θ = 2 and r = 5.

A: w=2zy-3xx=3θ+2r,y=3r2+θ, z =4r-θTo find ∂w∂r and ∂w∂θ for θ=2 and r=5