M129: Applied Calculus
M129 TMA Feedback Form
Q−1: [3+2 Marks] Let denotes the distance travelled by a body at time t:
a) Find instances when the body has zero velocity.
b) Find the acceleration of the body when it has zero velocity.
Q−2: [2+3 Marks] Find the slope of the tangent line to the following curves at the designated points:
a)
b)
Q¬−3: [2+3 Marks] Use the definition of the derivative to find f ′(x) if
a) .
b) .
Q¬−4: [2+2+1 Marks]Let .
a) Find the intervals on which the function f is increasing or decreasing and find the local extrema, if any.
b) Find the intervals on which the graph of fis concave up or concave down and find the points of inflection, if any.
c) What are the absolute maximum and minimum of f?
Q−5:[5 Marks] The dimensions of the of a swimming pool are x and y, its height is 3 m and its volume 300m3. Granite was installed on both and walls. The cost of one meter of granite is 4 rails. Find the dimensions of the such that cost is minimized.
Q¬−6:[2+3 Marks]
a) Find an equation of the tangent line to the curve
at x = 0.
b) Use the logarithmic differentiation to differentiate the function
Q¬−7:[5×1 Marks] Let P(t) be the population (in millions) of a certain city t years after 1990, and suppose that P(t) satisfies the differential equation P′(t) = 0.02 P(t), P(0)= 3
a) Find the formula for P(t).
b) What was the initial population (the population in 1990) ?
c) What is the growth constant?
d) What was the population in 1998?
e) How large is the population when it is growing at the rate 70000 people per year?
Q¬−8:[5 Marks] Find the area of the region bounded by the graphs
and .
حل واجبات الجامعة العربية المفتوحة O544321455 - OO966544321455
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حل واجبات الجامعة العربية المفتوحة O544321455 - OO966544321455
[email protected]
حل واجبات الجامعة العربية المفتوحة O544321455 - OO966544321455
[email protected]
حل واجبات الجامعة العربية المفتوحة O544321455 - OO966544321455
[email protected]
حل واجبات الجامعة العربية المفتوحة O544321455 - OO966544321455
[email protected]
حل واجبات الجامعة العربية المفتوحة O544321455 - OO966544321455
[email protected]
