What is the limit as (x,y) approaches (0,0) of (xycos(y))/(3x^2+y^2) ?

The limit as (x,y) approaches (0,0) of (xycos(y))/(3x^2+y^2) is diverges

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as (x,y) approaches (0,0) of (xycos(y))/(3x^2+y^2)

(x, y) \to (0, 0) lim (\frac{x y cos ( y )}{3 x ^{2} + y ^{2}})

diverges

Solution steps

(x, y) \to (0, 0) lim (\frac{x y cos ( y )}{3 x ^{2} + y ^{2}})

Find two different paths to approach the point that gives different values for the limit

Limit of

(x, y) \to (0, 0) lim (\frac{x y cos ( y )}{3 x ^{2} + y ^{2}})

along

x = 0 : 0

Limit of

(x, y) \to (0, 0) lim (\frac{x y cos ( y )}{3 x ^{2} + y ^{2}})

along

x = y : \frac{1}{4}

= diverges

7 - x^{2}

x \to 0 lim (4)

x \to 0 lim (\frac{x}{x ^{2} + x})

t \to 0 lim (e^{t})

y = 7 e^{x} + \frac{8}{3 x}

What is the limit as (x,y) approaches (0,0) of (xycos(y))/(3x^2+y^2) ?
The limit as (x,y) approaches (0,0) of (xycos(y))/(3x^2+y^2) is diverges