Barrons AP Calculus

(Marvins-Underground-K-12) #1
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f   (x) =   x
f (x) = ex

The curve   that    passes  through the point   (1, 1)  and whose   slope   at  any
point (x, y) is equal to has the equation
3 x − 2 = y
y^3 = x
y = x^3
3 y^2 = x^2 + 2
3 y^2 − 2x = 1
What is the domain of the particular solution in Question 19?
all real numbers
|x| ≤ 1
x ≠ 0
x < 0
x > 0

If   ,  k   a   constant,   and if  y   =   2   when    x   =   1   and y   =   4   when    x   =   e,  then,
when x = 2, y equals
2
4
ln 8
ln 2 + 2
ln 4 + 2
The slope field shown below is for the differential equation
y′ = x + 1
y′ = sin x
y′ = −sin x
y′ = cos x
y′ = −cos x
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