Sept 18
Recitation 2.7-2.8, 3.1-3.2
1
1. Find the equation of the tangent line to f (x) = 1+x
at x = 2.
ex
√
2. Find the second derivative of 3 xex
f (x + h) − f (x)
.
h→0
h
3. Draw a picture that explains the expression f 0 (x) = lim
Sept 18
Recitation 2.7-2.8, 3.1-3.2
√
d
4. Use the definition of the derivative to compute dx
2x + 1
5. Sketch a graph of a f (x) that has the following properties:
• f 0 (x) = 2 on the interval (1, ∞)
• Is continuous but not differentiable at x = 1
• Has a removable discontinuity at x = 0
• Has a jump discontinuity at x = −1
• lim f (x) = 0
x→−∞
Graph of f
3
2
1
−3
−2
−1
1
−1
−2
−3
2
3
2
Sept 18
Recitation 2.7-2.8, 3.1-3.2
6. .
7. Compute lim
x→2
2
1
− 2
x − 2 x − 2x
3
Sept 18
Recitation 2.7-2.8, 3.1-3.2
√
8. Compute lim 2x2 − x4 + 1
x→−∞
4