Review Exercises. 1. Find the indicated partial derivatives. Use the Product, Quotient, and/or Chain rules as needed. Do not simplify a) -V4x5 – 7xy + 2x + y³ дх 2x3-2y3. b) (8y³x2 – 5y? + 2x – 10)* ду c) ) (2*³-2y³. d) 4y - If f(x) = -10ln find: e) fx(x,y) дх 4y y* f) fy(x, y) g) fx(2,1) h) fy(0,2) If f(x,y) = ye2x-4y %3D find: i) fx(x, y). j) fy(x,y) k) fx(1,0) 1) fy(2,1) a) 20x*-7y+2 Зx2 3(4x5-7xy+2x+y³)²/3 -20x e) x2+7 b) 4(8y³x² – 5y? + 2x - 10)3 (24y²x² – 10y) d) c) 2y 2y2 y 40 f) g) -40/11 h) 20 i) 2ye2x-4y 1) -3 j) (1 – 4y)e2x-4y k) 0 2. Find each limit, some of them will require the use of L'Hospital's Rule (be sure to justify why the rule applies). Write ∞ or -∞ when appropriate. ex-1 a) lim х30 ex-1 b) lim Inx Inx Inx x2 х2 c) lim X o X-1 d) lim- х>1 х-1 e) lim x0+ x-1 f) lim x-1+ Inx g) lim x→0+ Inx et et h) lim i) lim j) lim a) 1 b) o c) 0 d) 1 e) o f) 00 g) 0 h) o i) o j) 0 2. Use the first and second derivatives of each function to determine critical points, intervals of increasing/decreasing. oints of inflection, intervals of concave up/concave down. Determine the domain, find the x- and y-intercepts, and use points of memine the equation of all asymptotes. Use this information to analyze sketch the graph. Label all important nts and any horizontal and vertical asymptotes. DO NOT GRAPH IN YOUR CALCULATOR b) f (x) = x³ – 6x² + 9x c) g(x) = %3D х d) f(x) = a) f(x) = -x+ – 6x² Inx %3D x2+1 e) f(x) = *+1 %3D 4. Section 14.2 problems 88 and 90 (Applied problems on partial derivatives) X-1
Review Exercises. 1. Find the indicated partial derivatives. Use the Product, Quotient, and/or Chain rules as needed. Do not simplify a) -V4x5 – 7xy + 2x + y³ дх 2x3-2y3. b) (8y³x2 – 5y? + 2x – 10)* ду c) ) (2*³-2y³. d) 4y - If f(x) = -10ln find: e) fx(x,y) дх 4y y* f) fy(x, y) g) fx(2,1) h) fy(0,2) If f(x,y) = ye2x-4y %3D find: i) fx(x, y). j) fy(x,y) k) fx(1,0) 1) fy(2,1) a) 20x*-7y+2 Зx2 3(4x5-7xy+2x+y³)²/3 -20x e) x2+7 b) 4(8y³x² – 5y? + 2x - 10)3 (24y²x² – 10y) d) c) 2y 2y2 y 40 f) g) -40/11 h) 20 i) 2ye2x-4y 1) -3 j) (1 – 4y)e2x-4y k) 0 2. Find each limit, some of them will require the use of L'Hospital's Rule (be sure to justify why the rule applies). Write ∞ or -∞ when appropriate. ex-1 a) lim х30 ex-1 b) lim Inx Inx Inx x2 х2 c) lim X o X-1 d) lim- х>1 х-1 e) lim x0+ x-1 f) lim x-1+ Inx g) lim x→0+ Inx et et h) lim i) lim j) lim a) 1 b) o c) 0 d) 1 e) o f) 00 g) 0 h) o i) o j) 0 2. Use the first and second derivatives of each function to determine critical points, intervals of increasing/decreasing. oints of inflection, intervals of concave up/concave down. Determine the domain, find the x- and y-intercepts, and use points of memine the equation of all asymptotes. Use this information to analyze sketch the graph. Label all important nts and any horizontal and vertical asymptotes. DO NOT GRAPH IN YOUR CALCULATOR b) f (x) = x³ – 6x² + 9x c) g(x) = %3D х d) f(x) = a) f(x) = -x+ – 6x² Inx %3D x2+1 e) f(x) = *+1 %3D 4. Section 14.2 problems 88 and 90 (Applied problems on partial derivatives) X-1
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Was hoping you could work some of these harder problems to show how the work. I have the answers I just don't know how to solve them.
Transcribed Image Text:Review Exercises.
1. Find the indicated partial derivatives. Use the Product, Quotient, and/or Chain rules as needed. Do not simplify
a) -V4x5 – 7xy + 2x + y³
дх
2x3-2y3.
b) (8y³x2 – 5y? + 2x – 10)*
ду
c) )
(2*³-2y³.
d)
4y
-
If f(x) = -10ln find: e) fx(x,y)
дх
4y
y*
f) fy(x, y)
g) fx(2,1)
h) fy(0,2)
If f(x,y) = ye2x-4y
%3D
find: i) fx(x, y). j) fy(x,y)
k) fx(1,0)
1) fy(2,1)
a)
20x*-7y+2
Зx2
3(4x5-7xy+2x+y³)²/3
-20x
e)
x2+7
b) 4(8y³x² – 5y? + 2x - 10)3 (24y²x² – 10y)
d)
c)
2y
2y2 y
40
f)
g) -40/11 h) 20
i) 2ye2x-4y
1) -3
j) (1 – 4y)e2x-4y
k) 0
2. Find each limit, some of them will require the use of L'Hospital's Rule (be sure to justify why the rule applies). Write
∞ or -∞ when appropriate.
ex-1
a) lim
х30
ex-1
b) lim
Inx
Inx
Inx
x2
х2
c) lim
X o X-1
d) lim-
х>1 х-1
e) lim
x0+ x-1
f) lim
x-1+ Inx
g) lim
x→0+ Inx
et
et
h) lim
i) lim
j) lim
a) 1 b) o
c) 0
d) 1
e) o
f) 00
g) 0
h) o
i) o j) 0
2. Use the first and second derivatives of each function to determine critical points, intervals of increasing/decreasing.
oints of inflection, intervals of concave up/concave down. Determine the domain, find the x- and y-intercepts, and use
points of memine the equation of all asymptotes. Use this information to analyze sketch the graph. Label all important
nts and any horizontal and vertical asymptotes. DO NOT GRAPH IN YOUR CALCULATOR
b) f (x) = x³ – 6x² + 9x
c) g(x) =
%3D
х
d) f(x) =
a) f(x) = -x+ – 6x²
Inx
%3D
x2+1
e) f(x) = *+1
%3D
4. Section 14.2 problems 88 and 90 (Applied problems on partial derivatives)
X-1
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