delta x taken from x sub k equal to a to x sub k equal to b minus delta x equals the integral from a to b of small f of xdx equals capital F of x between limits a and b equals capital F of minus capital F of a equals capital A
•x approaches x nought; or x tends to x nought
•the logarithm of c to the base b is equal to n
•the limit of f of x tends to x nought is not equal to f of x nought
11.1.5.Insert a proper word
1.Open interval can be shown by . . . .
a)parentheses
b)brace
c)point
2.Closed interval can be shown by . . . .
a)square brackets
b)brace
c)round brackets
3.Half open interval can be shown by . . . .
a)brackets
b)round brackets on the left and square brackets on the right
a)infinity
Tasks.
1. Analyse and memorize
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a)ϕ of z is equal to b, square brackets, parenthesis, z divided by c sub m plus two, close parenthesis, to the power of m over m minus 1, minus 1, close square brackets.
b)ϕ оf z is equal to b, multiplied by the whole quantity: the quantity two plus z over c sub m, to the power m over minus 1, minus 1.
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The absolute value of the quantity ϕ subj of t sub one, minus ϕ sub j of t sub two is less than or equal to the absolute value of the quantity M of t sub one minus β over j, minus M of t sub two minus β over j
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k = max ∑aij (t); t [a,b]; j =1,2....n |
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K is equal to the maximum over j of the sum from i equals one to i equals n of the modulus of a sub i j of t, where t lies in the closed interval a, b and where j from one to n.
limn→∞ |
∫t {f [sϕn (s)]+ ∆n (s)} |
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f [sϕ (s)] ds |
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The limit as n tends to infinite of the integral of f of s and ϕn of s plus delta sub n of s, with respect to s, from τ to,is equal to the integral of f of s and ϕ of s, with respect to s, from τ to.
Ψn − rs+1 (t)= etλq+s pn−rs +1
Ψ subn minus r sub s plus one of t is equal to p sub n minus r sub s plus 1 times e to the power t times λ sub q plus s.
L+n g = (−1)n (a0 g )(n) + (−1)(n−1)(ag n+1 +... + an g )
L sub n adjoint of g is equal to the minus one to the n, times the n-th derivative of a sub zero conjugate times g, plus, minus one to the n minus one, times the n minus first derivative of a sub one conjugate times g plus and so on to plus a sub n conjugate times g.
dF |
λi(t),t |
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λi(t),t |
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λi,(t)+ |
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The partial derivative of F of lambda sub i of t and t with respect to lambda, multiplied by lambda sub i prime of t plus the partial derivative of F with arguments lambda sub i of t and t, with respect to t, is equal to zero.
dds2 2y + [1+ b(s)] y = 0
The second derivative of y with respect to s plus y times the quantity 1 plus b of s is equal to zero
f (z)=ϕ€mk + 0(z −1 );(z → ∞;arg z = γ )
f of z is equal to ϕ sub mk hat plus big O of one over the absolute value of z, as absolute z becomes infinite, with the argument of z equals gamma.
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Dn−1 |
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D sub n minus one prime of x is equal to the product from s equal zero to n of, parenthesis, one minus x sub s squared, close parentheses, to the power epsilon minus one.
Κ(t, x)= |
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K of t and x is equal to one over two πi times the integral of K of t and z, over w minus w of x, with respect to w along curve of the modulus of w minus one half, is equal to rho.
d 2u + a4∆∆u = 0;(a > 0) dt 2
the second partial (derivative) of u with respect to t plus a to the fourth power, times the Laplacian of the Laplacian of u, is equal to zero, where a is positive
D (x)= |
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ζ k (w) |
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Пi c−∫i∞ |
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D sub k of x is equal to one over two πι times integral from c minus ι infinity to c plus i infinity of dzeta to the k of w, x to the w over (or: divided by) w, with respect to w, where c is greater than one.
2. Practice reading the following expressions by yourself, check your answer using the keys
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15 |
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b. |
lim f (x)= L |
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f '(x)= lim |
f (x + S )x − f (x) |
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e.∫ f (x)dx = F (x)+ c
f.x = (− ∞;+∞)
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f (x)dx = F(x) |
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lim ∑ |
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h. |
lg a3n = lg x = lg |
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i. |
M = |
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P, g; g ≠ 0 |
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Check your answer
a.Two seventh times – brace open – fifteen, plus seven times – bracket open – one half plus three times – parenthesis open – x minus two parenthesis, bracket, brace closed – equals five and two thirds, plus three quarters x
b.The limit of f of x as x tends to x sub one is capital l
c.f prime (or: α as h) of x is limit of f of x plus delta x minus f of x over delta x as delta tends to zero
d.S dot equals ds by dt
e.The integral of small f of x dx equals capital F of x plus capital O if capital F prime is equal to small f of x
f.Capital X equals the open interval minus infinity; plus infinity
g.The limit for delta x tending to zero, of the sum of small f of x sub k delta x taken from x sub k equal to a to x sub k equal to b minus delta x equals the integral from a to b of small f of xdx equals capital F of x between limits a and b equals capital F of minus capital F of a equals capital A
h.The logarithm of a to the power of three n equals the logarithm of the square root of x minus logarithm of the nth power of the fraction a squared over c
i.Set of all fractions p/g where p and g are elements of the set of integers and g cannot be zero
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