Problem #9: Which of the following functions is continuous at (0,0)? () S(x, y) = x...
' + 5y6 if (x, y) = (0,0) Which of the following functions is continuous at (0,0)? (i) f(x,y) = if (x, y) = (0,0) Xy5 0 (ii) g(x, y) = xo + 2y if (x, y) + (0,0) if (x, y) = (0,0) 0 V2 + y2 +9 - 3 *++y? (iii) h(x, y) = if (x, y) + (0,0) 3 if (x, y) = (0,0) (A) (i) only (B) (ii) only (C) all of them (D) (i) and...
Problem #2: Which of the following sets of functions are linearly independent on the interval (-0, c.)? [2 marks] (i) f1(x) = x, f2(x) = 4x, 13(x) = = x2 +6 (ii) f1(x) = 2e2x, 12(x) = 4e4x, f3(x) = 8e8x (iii) f1(x) = 8sinx, 12(x) = 4cos 2x, f3(x) 9 (A) (i) and (iii) only (B) (iii) only (C) none of them (D) (ii) only (E) all of them (F) (i) only (G) (i) and (ii) only (H) (ii)...
Q2. x+y (a). Let f(x,y) = x²+y²+1 Find (i). lim (x,y)-(1,1) f(x,y) (ii). lim f(x,y) (x,y)-(-1,1) (iii). lim f(x,y) (x,y)-(1,-1) (iv). lim f(x,y) (x,y)-(0,0) ( 4x²y if (x, y) = (0,0) Q3. Let f(x,y) = x2 + y2 1 if (x,y) = (0,0) Find (i). lim f(x,y) (x,y)--(0,0) (ii). Is f(x,y) continuous at (0,0)? (iii). Find the largest set S on which f(x,y) is continuous.
Q1. Let z = f(x,y) -√4x² – 2y² Find (i). domain of f(x,y) (ii). range of f(x,y) (iii). f(1,1) (iv). The level curves of f(x,y) for k = 0,1,2 4x2y Q3. Let f(x,y) = x2+y2 if (x,y) = (0,0) 1 if (x,y) = (0,0) Find (i) lim limf(x,y) (x,y)-(0,0) (ii). Is f(x, y) continuous at (0,0)? (iii). Find the largest set S on which f(x,y) is continuous.
Please answer part a and b :) Which of the following vector fields are conservative? (i) F(x, y) = (9y8 +3) i + (8x8y' +7) j (ii) F(x,y) = (8ye8x + cos 3ji + (e8x + 3x sin 3jj (iii) F(x,y)-7y2e7xyİ + (7 +xy) e7xyj (A) all of them (B) (iii) only (C) (i) and (ii) only (D) (i) and (iii) only (E) none of them (F) (ii) and (iii) only (G) (ii) only (H) (i) only st Save Submit...
21. Is the following function continuous at (0,0)? Hint:lim 1-cos T (1-cos(x2 +y2) f(x, y)=11-cosztym if(x,y) (0,0) if (x,y) = (0,0)
Let S = {1 + 3x, 1 − 5x2}. Which of the following polynomials could be added to the set S to form a basis for P2? (i) 2 + 3x − 6x2 (ii) 4 + 3x − 16x2 (iii) 9 + 15x − 21x2 (A) all of them (B) (i) and (ii) only (C) (i) and (iii) only (D) (ii) and (iii) only (E) none of them (F) (i) only (G) (ii) only (H) (iii) only
Let S = {1 + 3x, 1 − 5x2}. Which of the following polynomials could be added to the set S to form a basis for P2? (i) 2 + 3x − 6x2 (ii) 4 + 3x − 16x2 (iii) 9 + 15x − 21x2 (A) all of them (B) (i) and (ii) only (C) (i) and (iii) only (D) (ii) and (iii) only (E) none of them (F) (i) only (G) (ii) only (H) (iii) only
4. Let F(x,y) - PiQj be a smooth plane vector field defined for (x,y) f (0,0), and F - dr for integer j, and all suppose Q - Py for (z, y) (0,0). In the following L-JF dr for integer j, and all G are positively oriented circles. Suppose h = π where G is the circle x2 + y2-1. (a) Find 12 for G : (x-2)2 + y-1. Explain briefly. (b) Find Is for Cs: ( -2)y 9. Explain...
x?sin’y If the function f(x y)= { x2 +2V2' (x,y) (0,0) is continuous at (0,0), then (x y) = (0,0) AK) Ox= 1/2 0-1 .k=0 ok=2 ok=1