xy Let f(x,y) = x, if (x, y) + 0 (0, if (x, y)=(0,0) a. Show...

 

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xy Let f(x,y) = x²², if (x, y) + 0 (0, if (x, y)=(0,0) a. Show that fis continuous at (0, 0). b. Show that(x, 0) = x V x, and c. Show that (0,0) # (0,0). дудх If = th дхду (0,y) = - =y\y. , find the value of n for which the relation (2) (200) = 3 i If u log(x + y + z3 - 3xyz), show that 9 a. + + u = - (x+y+z)2* b. azu a²u a²u + + dx2 ay2 az² a²u +2+2- +2 дудг ди дудх a²u 9 дядя (x+y+z)2 Verify Euler's theorem for the function: a. (x + y) +y) (x + y) b. sin-1x n−1 + tan¹× c. log (x²+2). 12.If u = csc-1(x+y is true. . Prove that x² azu \x3+y³ ax2 +2xy a²u дудх +y202μ tan u Jy2 144 (13+ tan² u) 13 a. If u = zx ,v= , W= ,then show that (u,v,w) a(x,y,z)) = 4 b. If xp cos,y=psino,z=z, show that ǝ(u,v,w) =P a(p.,z)) 14. a.lf z = f(x, y), where x =u2v2 and y = 2uv, prove that a2z a2z Ju² Jv2 + =4(u² + v²). a²z ax² ay2 J²z + ди ди ди b. If u =(x-y,y-z,z-x), show that + + = 0 ax ay dz c. If z f(x,y), where xe" -e" and y = e-"-e", show that дг az Əz Əz Ju = x -y dv дх ду xy Let f(x,y) = x²², if (x, y) + 0 (0, if (x, y)=(0,0) a. Show that fis continuous at (0, 0). b. Show that(x, 0) = x V x, and c. Show that (0,0) # (0,0). дудх If = th дхду (0,y) = - =y\y. , find the value of n for which the relation (2) (200) = 3 i If u log(x + y + z3 - 3xyz), show that 9 a. + + u = - (x+y+z)2* b. azu a²u a²u + + dx2 ay2 az² a²u +2+2- +2 дудг ди дудх a²u 9 дядя (x+y+z)2 Verify Euler's theorem for the function: a. (x + y) +y) (x + y) b. sin-1x n−1 + tan¹× c. log (x²+2). 12.If u = csc-1(x+y is true. . Prove that x² azu \x3+y³ ax2 +2xy a²u дудх +y202μ tan u Jy2 144 (13+ tan² u) 13 a. If u = zx ,v= , W= ,then show that (u,v,w) a(x,y,z)) = 4 b. If xp cos,y=psino,z=z, show that ǝ(u,v,w) =P a(p.,z)) 14. a.lf z = f(x, y), where x =u2v2 and y = 2uv, prove that a2z a2z Ju² Jv2 + =4(u² + v²). a²z ax² ay2 J²z + ди ди ди b. If u =(x-y,y-z,z-x), show that + + = 0 ax ay dz c. If z f(x,y), where xe" -e" and y = e-"-e", show that дг az Əz Əz Ju = x -y dv дх ду

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a To show that f is continuous at 0 0 we need to show that the limit of fx y as x y approaches 0 0 e... View the full answer