Real Analysis II Please solve problems in few lines as given sample 2. Let ƒ: R² → R where f(x, y) = √1 - x² - y² and c = (0,-2).(a) Find and simplify Df(c).(b) Find and simplify f(c)+L((x, y) — c).-(c) What is the equation of the tangent plane to the graph of z =√1 - x² - y² through the point (0, -2, f(c))? 10:41←Expert Answer ⒸStep1a)⇒Step2b)(a)afdx(c)afay=)=(b) f(c) + L ((x, y) = c)andHence,f (x, y) ===>z =D f(c) = (cat))ale)2xg=2 yəgax=)93az8+ (4,4) (x-2, 4-2)8 + 4(x-2) + 4 (5-2).2x² + y²-1equation of=a)x² + y2x² + y²_z = 0a = 4afaxat 10 =4x + 4y-2 = 8?= (4,4)(2² +2²)+L((x,y)-(2,23)8 + L ((x-2, y-2))2325 = 23ayC = (2,2)= 4f(c) = 8tangent plane4 (x-2) + + (y-2) -1 (2-8) = 0ag=>- 3x1.-axIS29dy√x= 4Equation of this plane(x-) +33 (5-2)-1 (2-0) = 08

(a) Given fx,y=1-x2-y2, c=0,-22 ∂f∂x=-2x21-x2-y2∂f∂x0,-22=0∂f∂y=-2y21-x2-y2∂f∂y0,-22=221-0-12=1…

. Let f: R²R where f(x, y) = √√√1-x² - y² and c = (0, -2). (a) Find and simplify Df(c). (b) Find and simplify f(c) + L((x, y) — c). (c) What is the equation of the tangent plane to the graph of z = √1-2² - y² through the point (0, -, f(c))?

. Let f: R²R where f(x, y) = √√√1-x² - y² and c = (0, -2). (a) Find and simplify Df(c). (b) Find and simplify f(c) + L((x, y) — c). (c) What is the equation of the tangent plane to the graph of z = √1-2² - y² through the point (0, -, f(c))?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.4: Definition Of The Derivative

Problem 6YT

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Question

Real Analysis II Please solve problems in few lines as given sample

2. Let ƒ: R² → R where f(x, y) = √1 - x² - y² and c = (0,-2).
(a) Find and simplify Df(c).
(b) Find and simplify f(c)+L((x, y) — c).
-
(c) What is the equation of the tangent plane to the graph of z =
√1 - x² - y² through the point (0, -2, f(c))?

10:41
←
Expert Answer Ⓒ
Step1
a)
⇒
Step2
b)
(a)
af
dx
(c)
af
ay
=)
=
(b) f(c) + L ((x, y) = c)
and
Hence,
f (x, y) =
=
=>
z =
D f(c) = (cat))
ale)
2x
g=
2 y
əg
ax
=)
93
az
8+ (4,4) (x-2, 4-2)
8 + 4(x-2) + 4 (5-2).
2
x² + y²
-1
equation of
=
a
)
x² + y2
x² + y²_z = 0
a = 4
af
ax
at 10 =
4x + 4y-2 = 8
?
= (4,4)
(2² +2²)+L((x,y)-(2,23)
8 + L ((x-2, y-2))
23
25 = 23
ay
C = (2,2)
= 4
f(c) = 8
tangent plane
4 (x-2) + + (y-2) -1 (2-8) = 0
ag
=>
- 3x1.-
ax
IS
29
dy
√x
= 4
Equation of this plane
(x-) +33 (5-2)
-1 (2-0) = 0
8

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

Expert Solution