حل جميع واجبات الجامعة العربية المفتوحة
حل واجب m129 -------------- 0593565933-
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M129: Applied Calculus
Q−1: [4+1 Marks] let
a) Find the zeros of g(x) and h(x).
b) Find the points of intersection, if any, of the graphs of y = f (x) and
y = -4 .
Q−2: [2+2+1 Marks] Let .
a) Find f (g(x)) and describe its domain.
b) Find g (f (x)), and describe its domain
c) Describe the domains of f (x) and g(x).
Q−3: [2+3 Marks] Find the slope of the tangent line to the following curves at the designated points:
a)
b)
Q¬−4: [2+3 Marks] Use the definition of the derivative to find f ′(x) if
a) .
b)
Q¬−5: [5×1 Marks] Let
a) Find f ′(x) and f ′′(x).
b) Find the intervals on which f (x) is increasing or decreasing.
c) Find the local maximum and minimum of f (x), if any.
d) Find the intervals on which the graph of f (x) is concave up or concave down.
e) Find the points of inflection, if any.
Q−6: [5 Marks] A window is being built and the bottom is a rectangle and the top is a semicircle. If there is 12 m of framing materials what must the dimensions of the window be to let in the most light?
Q¬−7: [2+3 Marks]
a) Differentiate the function
b) Use the logarithmic differentiation to differentiate the function
Q¬−8: [5×1 Marks] Let P(t) be the population (in millions) of a certain city t years after 1950, and suppose that P(t) satisfies the differential equation P′(t) = 0.017 P(t), P(0)= 2560
a) Find the formula for P(t).
b) What was the initial population (the population in 1950) ?
c) What is the growth constant?
d) What was the population in 1960?
e) Estimate the population in the year 2020.
حل واجبات الجامعة العربية المفتوحة 0593565933-
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