Practice Questions
1. What is the derivative of
x10
?
10!
xn
gets small as n → ∞?
n!
x
x2
x x
Start with and
, possibly big. But we multiply by , , · · · which gets small.
1
2
3 4
1
3. Why is x the same as e−x ?
e
1 1
1
1
4. Why is e−1 = 1 − 1 + − + · · · between and ? Then 2 < e < 3.
2 6
3
2
2. How to see that
dy
= y starting from y = 3 at x = 0?
dx
Why is y = 3ex the right answer?
dy
6. Can you solve
= 5y starting from y = 1 at x = 0?
dx
Why is y = e5x the right answer?
5. Can you solve
7. Why does
eΔx − 1
approach 1 as Δx gets smaller?
Δx
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Resource: Highlights of Calculus
Gilbert Strang
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