1. One end of a 10 m long ladder is on the ground and the ladder is supported pa
ID: 2841002 • Letter: 1
Question
1. One end of a 10 m long ladder is on the ground and the ladder is supported partway along its length by resting on a top of 3 m high fence. If the bottom of the ladder is 4 m from the base of the fence and is been dragged along the ground away from the fence at a rate of 1/5 m/s, how fast is the free top end of the ladder moving (a) vertically downward and (b) horizontally to the right?
2. Two crates, A and B, are on the floor of a warehouse. The crates are joined by a rope 15 m long, each crate being hooked at floor level to an end of a rope. The rope is stretched tight and pulled over a pulley P that is attached to a rafter 4 m above a point Q on the floor directly between the two crates (see the diagram below). If crate A is 3 m from Q and is being pulled directly away from Q at a rate of 1/2 m/s, how fast is crate B moving toward Q ?
3. The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm.
(a) Use differentials to estimate the maximum error in the calculated area of the disk.
(b) What is the relative error? What is the percentage error ?
4. (a) Find the linearization L(x) of f(x) = x at a = 1 and then find for what values of x the approximation f(x) ' L(x) is accurate within 0.5.
Find the Taylor polynomial T3(x) of f(x)= ln/x x>0 about x=1
4.(a) Find the linearization L(x) of f(x) = x at a = 1 and then find for what values of x the approximation f(x) ' L(x) is accurate within 0.5.
5.f(x) = x ? 2ln(x2 + 3).
(a) Find the intervals of increase and decrease.
(b) Find the local maximum and minimum values of f.
(c) Find the inflection points and the intervals of concavity.
(d) Use the above steps to sketch the graph of f.
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