%EA 1₁.1₁.Let f(x,y)==This optionlim f(x, y) = 1.(x,y) →(0,0)=lim f(x, y) doesn't exist.(x,y)→(0,0)This option|||ThenNone of theseO(0) A: V

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Answered: Let f(x,y)= x-2y² Then

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
flx) = Jx-7 Lim f(3+h)-f(3) ||
Consider the function f defined by 22+y² V²+y?+1-1 f(r,y) = lim(7.y)-(0,0) f(x, y) =
ry Let f(r, y) and let L = lim(,1) >(0,0) f(x, y). Which of the following statements is correct? %3| 6x2 + 9y2 ry Türkçe: Eğer f(x, y) ve L 6x2 + 9y2 lim(7,1) »(0,0) f(x, y) ise aşağıdaki cümlelerden hangisi doğrudur?
II. Determine whether or not the function x² + 2y if (x, y) + (0,0) f (x, y) = 1 et-y 2 if (x, y) = (0,0) is continuous at (0, 0). If discontinuous, identify the type of discontinuity.
The equation for the line tangent to f (x) at the point (7, 11) is given by y = 12x – 9. Use %3D f(7 + h) – f(7) this to find lim h-0 h f(7 + h) – f(7) = 12 | lim h0 h f(7+ h) – f(7) lim h→0 h f(7+ h) – f(7) lim h→0 11 %3D f(7+ h) – f(7) _7 lim h→0 h f(7+ h) – f(7) lim h→0 does not exist.
II. Let g(x, y) = 47² +9y² (2x-3y)2 1. Show that lim g(x,y) does not exist. (2.) (0,0) 2. Is g(x,y) continuous at (0,0)? Why or why not?
Vx-2 5. lim x→2+ Vx²-4
ry Let f(x, y) and let L = lim(2.1) >(0,0) f(x, y). Which of the following statements is correct? 3x2 + 8y? ry Türkçe: Eğer f(x, y) = ve L = lim(zy) (0,0) f(r, y) ise aşağıdaki cümlelerden hangisi doğrudur? 3z2 + 8y? O L=1/11 O L does not exist because the limit as (x.y) goes to (0,0) along the x-axis is different from the one along the y-axis. (x-ekseni ve y-ekseni üzerinde limitler farklı olduğu için L yoktur.) O L does not exist because the limit as (x.y) goes to (0,0) along the x-axis is different from the one along the line x=y. (x-ekseni ve x=y doğrusu üzerinde limitler farklı olduğu için limit yoktur.) L=0 L=3/8 O L does not exist because f(x.y) is not defined at (0,0). (f(x.y) fonksiyonu (0,0) noktasında tanımsız olduğu için L yoktur.)
Let f be a differentiable function such that f(x + y) = f(x)+ f(y) + 5xy and f(h) lim h0 h = 16. Find f'(2).
3. Let f(r. y) = (a) Find limf(r.y), if it exists. If it does not exist, explain why. (xv)+(-1,2) (b) Find lim f(x, y), if it exists. If it does not exist, explain why. (.)-(0.0) (c) Is f(x, y) continuous at (0,0)? Why or why not?
- 8x? 5æ2 + 5y2 if (x, y) + (0,0); Consider the function f(x, y) if (ӕ, у) —D (0, 0). 1. As (x, y) → (0, 0) along the x-axis, lim (x , y) → (0,0) f(x, y) 2. As (x, y) → (0, 0) along the line y = x, lim (x , y) → (0,0) f(x, y) 3. Given your answers above, which of the following statements are true? (Select more than one if appropriate.) O f(x, y) is continuous at (0, 0). O f(x, y) has a limit at (0, 0). O f(x, y) is not continuous at (0, 0). O f(x, y) does not have a limit at (0, 0). O More information is needed to conclude something about the limit or continuity of f(x, y) at (0, 0).

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