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Using Stokes's Theorem In Exercises 7-16, use Stokes’s Theorem to evaluate
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EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
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- Sh1 Advanced matharrow_forward(ii) Use Stokes' Theorem to evaluate F. dr, where F(x, y, z) = x²zi + xy²j + z²k and C is the curve of intersection of the plane x+y+z = 1 and the cylinder x² + y² = 9, oriented counterclockwise as viewed from above. 5 z 0+ -2 y 0arrow_forwardHeader & Footer Text Consider the vector-valued function = ( 4 cos(t) + 2 sin(t), -cos(t) + V5 4 sin(t), V105 f(t)%3D 20 V105 VI05 sin(e) (a) Compute the first derivative and the nmagnitude of the first derivative. (Hint: Make sure to simplify your answer for the magnitude as much as possible! There will be magic cancellations.) (b) Are ^r(t) and ^r0°(t) perpendicular for all t? (Hint: You do not need to compute the second derivative. Use the formula (1*OF)' = (*"(t) · (1) = 26"(1) · i'(1) and your answer from part a.) (c) Use your answer from part b. to compute the principal normal vector in termns of the second derivative r00(E). (Hint: Your answer should involve the symbol r 0t). Do not compute the second derivative).arrow_forward
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