questions

questions

1. Find the equation of the line passing through the points (3,−2) and (𝑥,𝑦) for

𝑦=(𝑥)=3𝑥2−6𝑥+11

if 𝑥=2.

2. Find the slope of the line passing through the points (3,−2) and (𝑥,𝑦) for

𝑦=(𝑥)=3𝑥2−6𝑥+11

if 𝑥=3+ℎ. What happens this slope as ℎ approaches to zero?

3. Compute

lim𝑥→4(𝑥2−7𝑥+52𝑥3−20𝑥−47)

4. Compute

lim𝑥→2(𝑥2−4𝑥3−8)

5. Compute

lim𝑥→−3(𝑥+5𝑥+3)

For problems 6 and 7 let

(𝑥)=2𝑥3−6𝑥2+12𝑥−4

6. Compute

lim𝑥→−3√(𝑥)3

7. Compute

lim𝑥→−33(𝑥−1)

8. Let

(𝑥)={𝑥2−2𝑥+2 𝑖𝑓 𝑥≤12𝑥−1 𝑖𝑓 𝑥>1

Is 𝑓 continuous at 𝑥=1?

9. Let

(𝑥)=3𝑥−1

when 𝑥≠2, and let 𝑓(2)=3. Is 𝑓 continuous at 𝑥=2?

10. Explain why the function

ℎ(𝑥)=|𝑥3−3𝑥+7|

is continuous.

Section: 2.1 Problem #4

4. f(x) = 3 + x 2

(a) (1, 4), (1 + h, 3 + (1 + h) 2 )

(b) (x, 3 + x 2 ), (x + h, 3 + (x + h) 2 )

Section: 2.2 Problem #6

6. Use the information in the figure above to plot the values of the functions 2 f , f − g and g f and their derivatives at x = 1, 2 and 3.