Dear Calculus Scholar-Enthusiasts

Here are some problems that did not make it onto exam A.  
As usual, use _ for subscripts and braces for grouping,
e.g, b_{712} means "b sub 712".  Use ^ similarly for
superscripts.		Best Wishes, "Prof. Jonathan"

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P1:  Write an eqn. for the tangent line to

	log_5(x) = y

at the point P := (25,2).

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P.2:  Positive numbers C and D are such that

	log_C(8) = D.

Compute log_C(2) and log_2(C).  Express your answers ITOf (In Terms
Of) the letters "C" and "D".

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P.3: Compute d/dx of  7^{3^x}  and of  19^{log(x)+tan(x)} and of
sin(x)·e^x  and of  cos(x)/[x³ + x² + 5].

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P.4: Compute the two tangent lines to the circle x²+y²=3² which
pass through the point P:=(5,2).

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P.5: Use implicit differentiation to compute the slope of the
tangent line to

	8x + x^5 = [y/Pi]³ + cos(y)

at the point Q:=(1, 2Pi).

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P.6: The related-rate "two carts connected by a rope over a pulley"
problem, with different numbers.

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P.7: Describe the domains of these three functions as open/closed
(possibly infinite) intervals:

	arcsin,		arccos,		arctan .

Now compute each fnc's derivative.

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P.8: Define the set of "dyadic rationals".  Let g be the "ruler fnc";
if x = p/q (in canonical form) is a dyadic rational, then

	g(p/q) := 1/q.

If x is NOT a dyadic rational, then g(x):=0.  Describe the
continuity set of g() using set-builder notation as

	CtySet(g) = {x in R |  YOU FILL IN THE CONDITION HERE}.

Remember that the above set-builder notation is read as

 "The set of all x in R such that" <YOU FILL IN THE CONDITION HERE>.

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P.9: Give a precise epsilon, delta definition of the assertion

	"lim_{t->3} f(t)    =   19".
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