Saturday, August 20, 2011
Requirements for Next Week: Aug. 22-26, 2011
Aug. 22, 2011 Monday
Math: TCWAG 6, pp. 112-113, nos. 12, 14, 20, 22, 24, 28 or 48 (not sure which, cross-ref it na lang with your notes), 59, 62.
Econ: Those good at World History, recite! ;) This is a good chance to raise those reci scores. :)
Chem: Long Test on acids, bases, hydrolysis, etc.
English: Ma'am Iona's gonna comment on our RT. ;;)
Aug. 23, 2011 Tuesday
STR: Intel Forms, and edited Research Plan. (Check your emails for Sir's comments on them. )
Aug. 24, 2011, Wednesday
Physics: Prac Test (?)
--> long weekend after! \:D/
Please comment if anything's missing/wrong. :)
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Math HW for TC7 people!
ReplyDeleteDefine f(g(x)) and determine the numbers at which f(g(x)) is continuous.
12. f(x) = sqrt(x+1); g(x) = cube root of x
14. f(x) = sqrt(x^2-1) / sqrt(4-x); g(x) = |x|
Find the domain of the function, and then deterine for each of the indicated intervals whether the function is continuous on that interval.
20. f(x) = [[x]]
(-1/2, 1/2)
(1/4, 1/2)
(1,2)
[1,2)
(1,2]
22. h(x) = 2x-3 if x <-2
= x-5 if -2 ≤ x ≤ 1
= 3-x if x > 1
(-infinity, 1)
(-2, +infinity)
(-2, 1)
[-2, 1)
[-2, 1]
24. F(y) = 1 / (3+2y-y^2)
(-1,3)
[-1,3]
[-1,3)
(-1,3]
Determine the largest interval (or union of intervals) on w/c the function f(g(x)) of the indicated exercise is continuous.
28. Exercise 4 on page 112
f(x) = sqrt(x); g(x) = x^2 + 4
*******************
59. Find the largest value of k for which the function defined by f(x) = [[ x^2 -2 ]] is continuous on the interval [3, 3+k).
62. Show that the intermediate-value theorem guarantees that the equation x^3 + x + 3 = 0 has a root between -2 and -1.
Correction: in case 48 talaga dapat, not 28 XD
ReplyDeleteFind the values of the constants c and k that make the function continuous on (-infinity, +infinity), and draw a sketch of the graph of the resulting function.
48. f(x) = x + 2c if x < -2
= 3cx + k if -2 ≤ x ≤ 1
= 3x - 2k if x > 1