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10.1.3. Match the columns |
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Υ Ι Χ |
a) |
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the integral of 2x dx is x2 |
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∫2xdx = x2 |
b) |
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exponential functions |
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3 |
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c) |
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y equals the negative square root of the |
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difference z squared minus x squared |
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4 |
y = |
11+ 7 |
d) |
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the intersection of Y and X |
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2 + 22 |
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y = − |
z 2 − x2 |
e) |
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y equals the sum of a (sub) K, x of the power of |
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k, taken k equal to zero to k equal 4 |
6 |
y = ln x |
f) |
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rational fractional functions |
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7 |
y = ∑axk |
g) |
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radical |
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4 |
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k =ak |
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10.1.4. Give the examples of the functions: |
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Model: |
Trigonometric function is Y=sin x |
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•rational integral functions
•rational fractional functions
•irrational functions
•exponential functions
•trigonometric functions
•inverse trigonometric functions
Unit 11.Expressions concerning intervals and limits
Look through the table and try to memorize it.
Signs |
reading |
(a, b) |
open interval a b |
[a,b] |
closed interval a b |
(a,b] |
half – open interval a b, open on the left and closed on the |
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right |
X = (− ∞;+∞) |
Capital x equals the open interval minus infinite plus |
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infinite |
X → x0 |
x approaches x nought; or x tends to x nought |
lim f (x) = L |
the limit of f x as x tends to x one is capital L |
x→x1 |
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lim f (x) ≠ f (x0 ) |
the limit of f of x tends to x nought is not equal to f of x |
x→x0 |
nought |
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lim an = 0 |
the limit of a sub n is zero as n tends to infinity |
x→∞ |
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11.1Assignments
11.1.1.Memorize the following words and word-groups:
open interval |
[`oupqn `Intqvql] |
открытый интервал |
closed interval |
[`klouzd `Intqvql] |
закрытый интервал, |
half – open interval |
[`hRf `oupqn `Intqvql] |
наполовину открытый |
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[`InfInIt] |
интервал |
infinite |
бесконечный, |
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[In`fInItI] |
бесконечно большой |
infinity |
бесконечность |
11.1.2. Read the signs
• |
(a,b] |
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half – open interval a b, open on the left and closed on the |
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right |
• |
− ∞ + |
Capital x equals the open interval minus infinite plus ten |
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X = ( |
; 10) |
y equals the tangent of x |
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Y=tg x |
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lim f (x) = L |
the limit of f x as x tends to x one is capital L |
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x→x1 |
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the limit of f of x tends to x nought is not equal to f of x |
• |
lim f (x) ≠ f (x0 |
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x→x0 |
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nought |
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• |
lim an |
= 0 |
the limit of a sub n is zero as n tends to infinity |
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x→∞ |
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11.1.3. Match the columns
1 |
23/6 |
a) |
x approaches x nought; or x tends to x |
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nought |
2 |
[a,b] |
b) |
improper fraction |
3 |
(a, b) |
c) |
closed interval |
4 |
x= (x0 ;+∞) |
d) |
x equals the open interval x nought plus |
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infinite |
5 |
X → x0 |
e) |
open interval a b |
6 |
x→x |
f) |
the limit of f x as x tends to x one is capital |
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lim f (x) = L |
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L |
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1 |
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7 |
lim f (x) ≠ f (x0 ) |
g) |
the limit of f of x tends to x nought is not |
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x→x0 |
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equal to f of x nought |
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8 |
lim an = 0 |
h) |
the limit of a sub n is zero as n tends to |
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x→∞ |
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infinity |
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11.1.4. Translate into Russian
•m equals R sub one multiplied by x minus P sub one round brackets opened, x minus a sub one, round brackets closed, minus P sub two round brackets opened, x minus a sub two, round brackets closed
•a is directly proportional to b
•The limit for delta x tending to zero, of the sum of small f of x sub k
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