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(a) Is the function f(x, y) = xy(x²-x²) when (x, y) = (0,0) and f(0, 0) = 4 continuous at origin. (b) Redefine if necessary to make it continuous at (0, 0). - a. not continuous: lim = 0 + 4 = f(0,0) b. continuous if f(0, 0) = 0

(a) Is the function f(x, y) = xy(x²-x²) when (x, y) = (0,0) and f(0, 0) = 4 continuous at origin. (b) Redefine if necessary to make it continuous at (0, 0). - a. not continuous: lim = 0 + 4 = f(0,0) b. continuous if f(0, 0) = 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2:22 西認 9 VOD 34 KB/S B21+B22+B23---MAT1001---CALCU... TUTORIAL-1 SOLVE THE FOLLOWINGS: 1 (a) Is the function f(x, y) = (x. y) # (0, 0) and f(0. 0) = 4 continuous at origin. (b) Rede fine if necessary to make it continuous at (0, 0). a. not continuous: lim = 0 + 4 = ƒ (0, 0) b. continuous if f(0. 0) = 0 yG 2 when If u = ea cos(a Inr) show that 2 a?u 1 a?u 1 du + ar ar2 r 3 If w = r" prove that xx + Wyy + = m(m + Dm-2 where r? = x² + y² + z². 4 Let z= x +2y2 and x =r cose. y=r sin o. (). ). «G). Find a. b. a d. ava0 arao b. 4r2 tan 6 c. 2x d. -4x cosec²0 Ans. a. 2y e. 2r sin 20 The altitude of a right circular cone is 15cm and is increasing at 0.2 cm/sec. The radius of the base is 10cm and is decreasing at 0.3 cm/sec. How fast is the volume changing? Find and given that T-I Page 1 Find and * given that w(x, y. 2)=f(x²+y²+z²) where x=r cos 0 - cos ø, y =r cos 0- sin o, z = r sin e. If ye = sin x, find and at (0, 0) | Ans.会= 1.=0 Find the extreme values of u = x y² – 5x² – 8xy – 5y?. Find the directional derivative of f(x, y, z) = 4e²->+: at the point (1, 1, –1) in the direction toward the point (-3, 5, 6). 10 Find the shortest distance from the origin to the plane x - 2y – 22 = 3. Ans. Shortest distance is 1 (from (0,0,0)) to the
Transcribed Image Text:2:22 西認 9 VOD 34 KB/S B21+B22+B23---MAT1001---CALCU... TUTORIAL-1 SOLVE THE FOLLOWINGS: 1 (a) Is the function f(x, y) = (x. y) # (0, 0) and f(0. 0) = 4 continuous at origin. (b) Rede fine if necessary to make it continuous at (0, 0). a. not continuous: lim = 0 + 4 = ƒ (0, 0) b. continuous if f(0. 0) = 0 yG 2 when If u = ea cos(a Inr) show that 2 a?u 1 a?u 1 du + ar ar2 r 3 If w = r" prove that xx + Wyy + = m(m + Dm-2 where r? = x² + y² + z². 4 Let z= x +2y2 and x =r cose. y=r sin o. (). ). «G). Find a. b. a d. ava0 arao b. 4r2 tan 6 c. 2x d. -4x cosec²0 Ans. a. 2y e. 2r sin 20 The altitude of a right circular cone is 15cm and is increasing at 0.2 cm/sec. The radius of the base is 10cm and is decreasing at 0.3 cm/sec. How fast is the volume changing? Find and given that T-I Page 1 Find and * given that w(x, y. 2)=f(x²+y²+z²) where x=r cos 0 - cos ø, y =r cos 0- sin o, z = r sin e. If ye = sin x, find and at (0, 0) | Ans.会= 1.=0 Find the extreme values of u = x y² – 5x² – 8xy – 5y?. Find the directional derivative of f(x, y, z) = 4e²->+: at the point (1, 1, –1) in the direction toward the point (-3, 5, 6). 10 Find the shortest distance from the origin to the plane x - 2y – 22 = 3. Ans. Shortest distance is 1 (from (0,0,0)) to the
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