Question

Find the limits, if exists

1. lim?→−6 ?^2 − ? + 4/6 − ? =

2. lim?→5 2? − 10 /(? − 5)(? + 3) =

3. lim?→−4 ?(?) , ?? ?(?) = { 2? + 5, ? < −1 /13 − ? 2 , ? ≥ −1

4. lim?→∞ 4?^3 − 5 /4?^2 + 3? − 1 =

Part II. Find the derivative of the function.

1. ? = 12?^3 + 2?^2 − ? + 3

2. ?(?) = (6? − 5)(2? − 7)

3. ℎ(?) = 8?/ 2? −3

4. ?(?) = 3(5?^2 − 4)^6

5. ? = 7 ln(4?^2 + 9)

6. given ?(?) = 5 /?^2 . find ?′′(−2).

Part III. Resolve: 1. Find the equation of the tangent line to the graph of ?(?) = 4?^3 − 5? − 5 in the point (−1, −6).

2. Let I be the income function given by ?(?) = 28? − 0.03?^2 , where ? is the number of sold items. ¿Wich is the income marginal (in dolars) when ? = 250 ?

3. Given ?(?) = 4?^3 − 7?^2 , ¿What are the critical numbers of ? ?

Part V. Find the indefinite integral.

1. ∫ (12?^3 − 3?^2 − 8) ?? =

2. ∫ (20? − 4 /?^3 ) ?? =

3. ∫(? 9 − 7√?)?? =

Part V. Evaluate the definite integral.

1. ∫ 4,0(6? + 5) ?? 4 0 5

2. ∫3,-1 (9?^2 − 4) ??

3. ∫ 2,1 (10? − 3/ ?^2 ) ??

Part VI. Find the area of the region limited by the graph of ?(?) = 9? 2 − 8? + 6, axis ? and vertical lines ? = 2 y ? = 4.

Part VII. resolve: Determine the total cost function ?(?), since the marginal given since the cost function ?’(?) = 320 + 10? − 0.009? 2 and that the fixed cost are $23,000.

Answer 1