Stark

If 𝑢 = 𝑓(𝑥 − 𝑦, 𝑦 − 𝑧, 𝑧 − 𝑥) show that 𝜕𝑢/𝜕𝑥 + 𝜕𝑢/𝜕𝑦 +𝜕𝑢/𝜕𝑧 = 0 Answer:-

4 a] Evaluate Answer:-

Find the extreme values of the function 𝑓(𝑥, 𝑦) = 𝑥 3 + 3𝑥𝑦 2 − 3𝑦 2 − 3𝑥 2 + 4 Answer:-

3 a] Expand Up to the term containing using maclaurin’s Series. Answer:-

2 c] Find the radius of curvature for the curve , where the curve meets the x-axis. Answer:-

2 b] Find the pedal equation of the curve . Answer:-

2 a] Show that the curves and cuts each other orthogonally. Answer:-

1 c] Find the radius of curvature of the curve at the point (a,0) Answer:-

1 b] Find the angle between the curves and