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Derivatives and Integrals (Ln and e) Flashcards | StudBud
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Derivatives and Integrals (Ln and e)
Derivatives and Integrals (Ln and e)
7 terms
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Mixed review of #derivatives #integrals #calculus #antiderivative #naturallogarithms #naturalbase
Flashcards
7 cards
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Questions
7
Answers
1
Find the area of the function f(x) = (e
2x
)/(e
2x
+ 3) from x = 0 to x = 3
-201.21
-4.62
-2.31
-402.43
2
Find the derivative: f(x)=ln (x
4
+2)/(5x)
f'(x) = (3x4 + 2)/(x(x4+2))
f'(x) = x4 - 5x + 2
f'(x) = (3x4 - 2)/(x(x4+2))
f'(x) = 4x3/5
3
Find the derivative: f(x) = e
5x-3
f'(x) = 5e5x-3
f'(x) = e5
f'(x) = 1/6 e^6
f'(x) = e5x-3
4
Find the derivative: f(x) = 2x e
6x+1
f'(x) = 12x e6x+1+ 2e6x+1
f'(x) = 2e6x+1
f'(x) = 12e6x+1
f'(x) = 2x e6x+1+ 2e6x+1
5
Solve the differential equation dy/dx = e
x
(e
x
- 2)
3
given that it passes through (0, 4)
y = 1/4(ex - 2)4 + 4.25
y = 3(ex - 2)2 + 1
y = 1/4(ex - 2)4 + 3.75
y = 3(ex - 2)2 + 7
6
Find the equation of the tangent line to the function f(x) = e
2x
- 1 at (2, 4)
y = 72.90x - 186.40
y = 54.60x + 113.20
y = 2e2x
y = 109.20x + 222.40
7
Find any relative extrema: y = e
x
- 3x
Minimum at (1.09, -0.30)
Maximum at (1.09, -2)
Minimum at (0, -1)
Maximum at (0, 1)
