MATH 157 Course Review
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Last updated 1:30 AM on 5/4/23
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43 Terms
1
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d/dx sin x
cos x
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d/dx cos x
\-sin x
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d/dx tan x
\-sec² x
4
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d/dx arccos x
\-1/√(1-x²)
5
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d/dx arcsin x
1/√(1 - x²)
6
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d/dx log x
1 / x ln a
7
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d/dx e^x
e^x
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d/dx |x|
x / |x|
9
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sin -π
0
10
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sin 0
0
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sin π/2
1
12
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sin π
0
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sin 3π/2
\-1
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sin 2π
0
15
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cos -π
\-1
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cos 0
1
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cos π/2
0
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cos π
\-1
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cos 3π/2
0
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cos 2π
1
21
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average cost function
C(x) / x
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marginal average cost function
d/dx( C(x) / x )
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revenue function
R(x) = px
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marginal revenue function
R’(x) = d/dx(px)
25
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demand function
q = f(p)
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elasticity of demand
E(p) = - p \* f’(p) / f(p)
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elastic
E(p) > 1
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inelastic
E(p) < 1
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unitary
E(p) = 1
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revenue function
R(p) = pq = pf(p)
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marginal revenue function
R’(p) = f(p) \* \[1 - E(p)\]
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differential
dy = f’(x) \* dx
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actual change in y
Δy = f(a + Δx) − f(a)
34
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what is the function of this surface?
z = e^x \* cos(y)
35
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what is the function of this surface?
z = sin(x - y)
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what is the function of this surface?
z = sin(xy)
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what is the function of this surface?
z = sin(x) - sin(y)
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what is the function of this surface?
z = (x - y) / (1 + x^2 + y^2)
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what is the function of this surface?
z = (1 - x^2)(1 - y^2)
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what is the function of this contour map?
pyramid
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what is the function of this contour map?
paraboloid
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what is the function of this contour map?
cone
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what is the function of this contour map?
sphere