- Compute Sy z(z−1)²(2²−1)dz where y is the circle |z – 2| = 5/2 with negative orientation.
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Q: please this is not meant by Ai
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- Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.Evaluate ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9 with positive direction using Green's Theorem.Evaluate | 2*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the plane x = -3.
- Evaluate LTY xy¹ ds where C' is the right half of the circle x² + y² = 9(b) Sketch the graph of the function y = 1+ /16 – x²2 for -4 < x < 4. Hint: x2 + y? = 16 is the equation of a circle in the ry plane with center (0,0) and radius 4.3. Find the equation of a circle with center at (2, 3) and tangent to the line 3x – 5y = 8. a. 2x? + 2y² – 8x – 12y + 9 = 0 b. 2x? + 2y? + 8x – 12y + 9 = 0 c. 2x? + 2y? – 8x + 12y + 9 = 0 d. 2x2 + 2y² – 8x – 12y – 9 = 0
- 10. Use the given conditions to write an equation for the circle C (-/3, -2), a= 2 O [(x+/3)] ^2 + [(y-2)] ^2 = 2 O [(x-2)] A2 + [(y-V3)] ^2 = 10 O [(x-/3)] ^2 + [(y+2)] ^2 = 10 O [(x+/3)] ^2 + [(y+2)] ^2 = 28. Is the point (2, –7) on the circle defined by (x + 6) + (y + 1) = 100?ort er 2x² + 2y² + 4x + 8y + 8 = 0 is the equation of a circle with center (h, k) and radius r for: h and k= and r =
- -(2) Calculate ge yde + xzªdy - zy³ dz, where c is the circle x² +9² = 4, Z=3 (conterclockwise) hit: F = 2 cost i + 2 sint sint j + 3R | § J. dF = (OXT). R. AIntegrate counterclockwise dz, C the circle with z2 + 16z + 63 center –7 and radius 2. - dz z² + 16z + 63The area of the upper half of the circle whose equation is (x – 1)2 + y2 = 1 is given by