Question

QUESTION NINE (a) Given the function $f(t) = 2t^2 - 3t + 4$, find $\frac{dy}{dt}|_{t=3}$ from the first principle. [7] (b) Find $\frac{dy}{dx}$ of the function $y = (3x - 2x^2)(5 + 4x)$. [5] (c) Evaluate the integral $\int 3x^3 dx$. [3] (d) Mr. Chimwemwe has a farm which uses bio energy for dairy machines operation. In the Annual Energy Outlook, the farm Information administrator projected the consumption C (in quadrillion of Btu per year) of petroleum to follow the model $C_1 = 0.004t^2 +$ $0.330t + 38.3, 0 \le t \le 30$ where $t = 0$ corresponding to 2000. If the actual consumption more closely follows the model $C_2 = 0.005t^2 + 0.301t + 38.2, 0 \le t \le 30$. How much petroleum would be saved? [5]

          QUESTION NINE
(a) Given the function $f(t) = 2t^2 - 3t + 4$, find $\frac{dy}{dt}|_{t=3}$ from the first principle.
[7]
(b) Find $\frac{dy}{dx}$ of the function $y = (3x - 2x^2)(5 + 4x)$.
[5]
(c) Evaluate the integral $\int 3x^3 dx$.
[3]
(d) Mr. Chimwemwe has a farm which uses bio energy for dairy machines operation. In the
Annual Energy Outlook, the farm Information administrator projected the consumption C
(in quadrillion of Btu per year) of petroleum to follow the model $C_1 = 0.004t^2 +$
$0.330t + 38.3, 0 \le t \le 30$ where $t = 0$ corresponding to 2000. If the actual
consumption more closely follows the model
$C_2 = 0.005t^2 + 0.301t + 38.2, 0 \le t \le 30$. How much petroleum would be saved? [5]

QUESTION NINE
(a) Given the function f(t) = 2t^2 - 3t + 4, find (dy)/(dt)|t=3 from the first principle.
[7]
(b) Find (dy)/(dx) of the function y = (3x - 2x^2)(5 + 4x).
[5]
(c) Evaluate the integral ∫ 3x^3 dx.
[3]
(d) Mr. Chimwemwe has a farm which uses bio energy for dairy machines operation. In the
Annual Energy Outlook, the farm Information administrator projected the consumption C
(in quadrillion of Btu per year) of petroleum to follow the model C1 = 0.004t^2 +
0.330t + 38.3, 0 ≤ t ≤ 30 where t = 0 corresponding to 2000. If the actual
consumption more closely follows the model
C2 = 0.005t^2 + 0.301t + 38.2, 0 ≤ t ≤ 30. How much petroleum would be saved? [5]

Added by Kelly B.

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