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$\dfrac{dy}{dx} = 1x + y$ and $y(1) = 3$ . Use one step of Euler's method with $h = 0.1$ to estimate $y(1.1)$ .
$\dfrac{dy}{dx} = y$ and $y(0) = 8$ . Use Euler's method with two steps of size $h = \tfrac{1}{2}$ to estimate $y(1)$ .
The solution of $\dfrac{dy}{dx} = y$ , $y(0) = 1$ , is concave up. Does Euler's method with $h > 0$ over- or underestimate $y(1)$ ?
1. Underestimate: each step follows a tangent line, which lies below a concave-up curve
2. Overestimate
3. It is exact
The solution of $\dfrac{dy}{dx} = y$ , $y(0) = 2$ , is concave up. Does Euler's method with $h > 0$ over- or underestimate $y(1)$ ?
1. Underestimate: each step follows a tangent line, which lies below a concave-up curve
2. Overestimate
3. It is exact
The solution of $\dfrac{dy}{dx} = y$ , $y(0) = 3$ , is concave up. Does Euler's method with $h > 0$ over- or underestimate $y(1)$ ?
1. Underestimate: each step follows a tangent line, which lies below a concave-up curve
2. Overestimate
3. It is exact
The solution of $\dfrac{dy}{dx} = y$ , $y(0) = 8$ , is concave up. Does Euler's method with $h > 0$ over- or underestimate $y(1)$ ?
1. Underestimate: each step follows a tangent line, which lies below a concave-up curve
2. Overestimate
3. It is exact
The solution of $\dfrac{dy}{dx} = y$ , $y(0) = 9$ , is concave up. Does Euler's method with $h > 0$ over- or underestimate $y(1)$ ?
1. Underestimate: each step follows a tangent line, which lies below a concave-up curve
2. Overestimate
3. It is exact
The solution of $\dfrac{dy}{dx} = y$ , $y(0) = 5$ , is concave up. Does Euler's method with $h > 0$ over- or underestimate $y(1)$ ?
1. Underestimate: each step follows a tangent line, which lies below a concave-up curve
2. Overestimate
3. It is exact
The solution of $\dfrac{dy}{dx} = y$ , $y(0) = 6$ , is concave up. Does Euler's method with $h > 0$ over- or underestimate $y(1)$ ?
1. Underestimate: each step follows a tangent line, which lies below a concave-up curve
2. Overestimate
3. It is exact
The solution of $\dfrac{dy}{dx} = y$ , $y(0) = 4$ , is concave up. Does Euler's method with $h > 0$ over- or underestimate $y(1)$ ?
1. Underestimate: each step follows a tangent line, which lies below a concave-up curve
2. Overestimate
3. It is exact
The solution of $\dfrac{dy}{dx} = y$ , $y(0) = 7$ , is concave up. Does Euler's method with $h > 0$ over- or underestimate $y(1)$ ?
1. Underestimate: each step follows a tangent line, which lies below a concave-up curve
2. Overestimate
3. It is exact
A population follows $\dfrac{dP}{dt} = \dfrac{ 7 }{10}P\left(1 - \dfrac{P}{ 558 }\right)$ . What is its carrying capacity?
$\dfrac{dP}{dt} = \dfrac{ 3 }{10}P\left(1 - \dfrac{P}{ 280 }\right)$ . For which population $P$ is it growing fastest?
The logistic solution $P(t) = \dfrac{ 203 }{1 + Ae^{-rt} }$ has $P(0) = 58$ . Find $A$ .
$P(t) = \dfrac{ 277 }{1 + 5e^{-0.3t} }$ . Find the initial population $P(0)$ .
$\dfrac{dP}{dt} = \dfrac{ 2 }{10}P\left(1 - \dfrac{P}{ 253 }\right)$ . How fast is the population growing when $P = \dfrac{ 253 }{2}$ ?

Answers

$\frac{17}{5}$
$18$
Underestimate: each step follows a tangent line, which lies below a concave-up curve
$558$
$140$
$\frac{5}{2}$
$\frac{277}{6}$
$\frac{253}{20}$