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Derivatives and Integrals (Ln and e) Flashcards | StudBud

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Derivatives and Integrals (Ln and e)

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Questions 10

Answers

1
Find any relative extrema: y = e^x - 3x
Maximum at (1.09, -2)
Minimum at (0, -1)
Maximum at (0, 1)
Minimum at (1.09, -0.30)
2
Find the derivative: f(x)=ln (x⁴+2)/(5x)
f'(x) = (3x4 - 2)/(x(x4+2))
f'(x) = x4 - 5x + 2
f'(x) = 4x3/5
f'(x) = (3x4 + 2)/(x(x4+2))
3
Find the integral: ∫ (e^3x- e^x+ 3)/(e^x) dx
(1/3)e3x - ex + 3x + C
ln (e3x - ex + 3)+ C
ln ex + C
(1/2)e2x - x - 3e-x + C
4
Find the equation of the tangent line to the function f(x) = e^2x- 1 at (2, 4)
y = 54.60x + 113.20
y = 2e2x
y = 109.20x + 222.40
y = 72.90x - 186.40
5
Find the integral: ∫ (2x+3)/(3x²+9x-11) dx
1/3 ln (2x+ 3) + C
1/3 ln (3x2+9x-11) + C
ln (3x2+9x-11) + C
ln (x3 + 9/2x2 - 11x) + C
6
Find the derivative: f(x) = e^5x-3
f'(x) = e5
f'(x) = e5x-3
f'(x) = 1/6 e^6
f'(x) = 5e5x-3
7
Find the area of the function f(x) = (e^2x)/(e^2x+ 3) from x = 0 to x = 3
-2.31
-201.21
-4.62
-402.43
8
Find the derivative: f(x) = 2x e^6x+1
f'(x) = 12x e6x+1+ 2e6x+1
f'(x) = 12e6x+1
f'(x) = 2e6x+1
f'(x) = 2x e6x+1+ 2e6x+1
9
Solve the differential equation dy/dx = e^x(e^x - 2)³given that it passes through (0, 4)
y = 3(ex - 2)2 + 7
y = 1/4(ex - 2)4 + 4.25
y = 3(ex - 2)2 + 1
y = 1/4(ex - 2)4 + 3.75
10
Find the integral: ∫ 2e^5x+9dx
(2/5)e5x+9 + C
2e5x+9 + C
e5x+9 + C
(5/2)e5x+9 + C