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( ) f b a b f a f b f x dx b a = ( ) 2 ( ) 4 3 f b a b f a f h Method 3 One could even use the Lagrange polynomial to derive Simpson's formula Notice any method of threepoint quadratic interpolation can be used to accomplish this task In this case, the interpolating function becomes ( ) 2 ( ) 2 ( ) 2 2 2 ( )( ) ( ) ( ) 2 ( ) 2 2Suppose f−1(x) = c, f−1(y) = d Then f(c) = x and f(d) = y and f(ac bd) = af(c) bf(d) = ax by Hence f−1(ax by) = ac bd = af−1(x) bf−1(y) Example 6) D set of all twice differential functions → set of all functions, L(f) = af00 bf0 cf Proof L(sf tg) = a(sf tg)00 b(sf tg)0 c(sf tg) = saf00 tag00 sbf0Let f (x)= (xa) (xb) (xc) then prove that f` (x)/f (x)=1/ (xa)1/ (xb)1/ (xc) pratham , 4 years ago Grade11 × FOLLOW QUESTION We will notify on your mail & mobile when someone answers this question Enter email id Enter mobile number 91

Prealgebra questions and answers;X 0 2=EShow that there is an unbounded continuous function f E!R Solution Consider the function f(x) = 1 x x 0 Since x 0 2= E, this function is continuous on E On the other hand, by the If we want to differentiate with the Quotient Rule f '(x) = (B Cex) d dxA −A d dx(B Cex) (B Cex)2 d dx A = 0, the derivative of a constant is zero d dx (B Cex) = Cex Thus, f '(x) = − ACex (B Cex)2 Answer link

If A and B are subsets of the real numbers R and f A !B is a function, then the average rate of change of f as x varies between x 1 and x 2 is the quotient average rate of change = y x = y 2 y 1 x 2 x 1 = f(x 2) f(x 1) x 2 x 1 (61) It's a linear approximation of the behavior of f between the points x 1 and x 2 7 Quadratic FunctionsRolle's Theorem Suppose that y = f(x) is continuous at every point of the closed interval a;b and di erentiable at every point of its interior (a;b) and f(a) = f(b), then there is at least one point c in (a;b) at which f0(c) = 0 The graphs of some functions satisfying the hypotheses of the theorem are shown below 14 12 10 8 6 4 2 Ð 2 Ð 4Given random variables,, , that are defined on a probability space, the joint probability distribution for ,, is a probability distribution that gives the probability that each of ,, falls in any particular range or discrete set of values specified for that variable In the case of only two random variables, this is called a bivariate distribution, but the concept generalizes to any

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Answer (1 of 5) f(x)=x Function is giving the absolute value of x whether x is positive or negative See the y axis of graph which is f(x) against x, as x axis It shows y axis values or f(x) is always positive whether x is positive or negative This function is an example of transfer functIf x ∈ f ( A) ∩ f ( B), then x = f ( a) and x = f ( b) for some a ∈ A and b ∈ B But then, by the assumption of injectivity, a = b, so a ∈ A ∩ B and x ∈ f ( A ∩ B) Let f X → Y be a oneone, and A, B ⊆ X We show that f (A ∩ B) = f (A) ∩ f (B) we need to prove that f (A) ∩ f (B) ⊆ f (A ∩ B) Let y ∈ f (A) ∩ f (B)Option a) 10 pm b) 100 pm c) 130 pm d) 230 pm Next Question A starts riding his bike at 10am with a speed of kmph and B also starts at 10am with a speed of 40kmph from the same point in the same direction

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An easy way to do these types of questions is considering the question into glasses means consider here that B fills 45 glasses in 45 minutes so A has to feel the same in 375 minutes that is it feels 45/375 glasses per minute which is equal to 12 glasses per minute in 30 minutes tab A will feel 30×12 glasses, that is 36 glasses now tap B $\begingroup$ By F(x), I mean the cumulative distribution function of x From the small hint in your comment, I'm guessing we can't simply use F(1/2) F(1/2) because the function is broken into two parts and so we are integrating over the= (xa)(xb) = x(xb)a(xb) = x²bxaxab We can stop here, or continue by taking 'x' as common in the middle term So, we get = x²x(ab)ab Therefore, it is in the form of ax²bxc Therefore, the expansion form of (xa)(xb) is x²x(ab)ab Thank you

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(b) X= S1 ×D2 with Aits boundary torus S1 ×S1 (c) X= S1 ×D2 and Athe circle shown in the figure (d) X= D 2∨D with Aits boundary S1 ∨S1 4 MATH 215B SOLUTIONS TO HOMEWORK 1 (e) X a disk with two points on its boundary identified and Aits boundary S 1∨S X is a variable and the cohost of BFB They were the host after Donut resigned until Four's return X's first appearance in BFB was in " Getting Teardrop to Talk " where they and Four started a competition to win "a BFDI " (a compilation of all season 1 and 2 episodes) X was also going to be the cohost of Battle for Dream Island The Power46 Bijections and Inverse Functions A function f A → B is bijective (or f is a bijection) if each b ∈ B has exactly one preimage Since "at least one'' "at most one'' = "exactly one'', f is a bijection if and only if it is both an injection and a surjection A bijection is also called a onetoone correspondence

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 Misc 43Choose the correct answerIf 𝑓﷐𝑎𝑏−𝑥﷯=𝑓﷐𝑥﷯, then ﷐𝑎﷮𝑏﷮𝑥 𝑓﷐𝑥﷯﷯𝑑𝑥 is equal to (A) ﷐𝑎𝑏﷮2﷯﷐𝑎﷮𝑏﷮ 𝑓﷐𝑏−𝑥﷯﷯𝑑𝑥 (B) ﷐𝑎𝑏﷮2﷯﷐𝑎﷮𝑏﷮ 𝑓﷐𝑏𝑥﷯﷯𝑑𝑥 ﷐𝑏 −𝑎﷮2﷯﷐𝑎﷮𝑏﷮ 𝑓﷐𝑥﷯﷯𝑑𝑥 (D) ﷐𝑎𝑏﷮2﷯﷐𝑎﷮𝑏X x a x b f x x a x k f x b a x f x f a f x f b η η π η = − − = − − = − − Stiprusis ekstremumas Aib ė M0 (stiprioji arba 0 eil ės aplinka) 0 ir , , , 0 max ( ) ( ) x a b M y y M y x y xε ε ∈ ɶ ɶ∈ > − < Funkcija y y x M= ∈( ) suteikia funkcionalui ( ) , ,( ) b a I y F x y y dx= ∫ ′ stipr ųjį ekstremum ąXk = X k x k!

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Since f(x) is continuous, by the Intermediate Value Theorem it takes every possible value between m and M In particular, there is atleast one place c at which the function f(x) hasa value equal to f(c) = ∫b a f(x)dx b a Multiplying bothsides by b a proves the result 4The first fundamental theorem of integral calculusExample Consider evaluating I(f)= Z π 0 excosxdx= − eπ1 2 = − In this case, f0(x)=excosx−sinx f00(x)=−2exsinx max 0≤x≤π ¯ ¯f00(x) ¯f00 (75π) ¯ = Then ET n(f)=− h2 (b−a) 12 f00 (cn) ¯EnT(f) ¯ ≤ h2π 12 = 3906h2 Also EeT n(f)=− h2Graph f(x)=b^x Find where the expression is undefined The domain of the expression is all real numbers except where the expression is undefined In this case, there is no real number that makes the expression undefined The vertical asymptotes occur at areas of infinite discontinuity

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 Putting f(x1) = f(x2) we have to prove x1 = x2 Putting f (x1) = f (x2) ⇒ (b1, a1) = (b2, a2) Hence, b1 = b2 & a1 = a2 Now, since a1 = a2 & b1 = b2 We can say that, (a1, b1) = (a2, b2) Hence, if f(x1) = f(x2) , then x1 = x2 Hence, f is oneone Check onto f A × B → B × A f(a, b) = (b, a) f(x) = (b, a) Let y = (b, a) Now, for every (b, a Answer is (ab)/2 int_a^b f(x) dx Let "I" be the integral, I = int_a^b xf(x) dx (1) Using the property of definite integrals, I = int_a^b (abx) f(abx) dx It is given that, f (abx) = f(x) implies I = int_a^b (abx) f(x) dx implies I = (ab) int_a^bf(x) dx int_a^b x f(x) dxDensity function (PDF) of Xis the function f X(x) such that for any two numbers aand bin the domain X, with a

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 Both f (1) and f (2)=2 There is c in (0,2) such that f' (c)=f (b)f (a)/ba By the MVT, there is a number c in (0, 1) such that f' (c) = f (1) f (0)/ (1 0) = 2/1 = 2 You can use the same idea to show that for another number c in (1, 2), f' (c) = 0 If you knew that f' was continuous, you could use the Intermediate Value Theorem to showA b c d e f g h i >JK< l m n o p q r s t u v w x y z 31 likes 1 talking about this Community Facebook is showing information to help you betterThe special case, when f(a) = f(b) is known as Rolle's TheoremIn this case, we have f '(c) =0In other words, there exists a point in the interval (a,b) which has a horizontal tangentIn fact, the Mean Value Theorem can be stated also in terms of slopes

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In particular, for all x2(p ;p ), f(x) >f(p) ">0 (b)Let EˆR be a subset such that there exists a sequence fx ngin Ewith the property that x n!Numerical Analysis Trapezoidal and Simpson's Rule Natasha S Sharma, PhD General Trapezoidal Rule T n(f) 1 We saw the trapezoidal rule T 1(f) for 2 points a and b 2 The rule T 2(f) for 3 points involves three equidistant points a, ab 2 and b 3 We observed the improvement in the accuracy of T 2(f) over T 1(f) so inspired by this, we would like to apply this rule to n 1 equally spacedThe parameter a can be added to or subtracted from the input x before the rule f is applied y = f(x) becomes y = f(x ± a) These transformations are called horizontal shifts or translationsThey move the graph of the given function left (adding positive a) or right (subtracting positive a)

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 PDF/X, PDF/A, PDF/VT, and PDF/E files can be created in various ways, such as by using Acrobat Distiller or the File > Save As Other command If you open a PDF that conforms to one of these standards, you can view the standards information in the Navigation pane ( Choose View > Show/Hide > Navigation Panes, and then click the Standards8 Newton's advancing X k ∆kf(a) k!∆kf(a) = f(ax) real a,x difference formula f = polynomial 9 Euler's summation X a≤k

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The CDC AZ Index is a navigational and informational tool that makes the CDCgov website easier to use It helps you quickly find and retrieve specific information Stack Exchange network consists of 178 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack ExchangeAt 0 am, Preetha follows her from Divya's house on her bicycle at 8 kms per hour When will divya be 1 km behind Preetha?

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 The position of a moving car at time t is given by f(t) = at^2 bt c, t > 0, where a, b and c are real numbers greater than 1 asked in Mathematics by Anjali01 ( 476k points) jee main b(x) = g(x) 4 This object is a pull tab Answer Have students come up and move the red parabola as indicated in the function There is a black parabola underneath that holds the original position You can flip the parabola by clicking on it and going to "flip" Slide 28 / 113I came to the US from China with a bachelor's degree in Physics from ShanXi Normal University I received my Master's Degree in Computer Science from University of Nevada, Reno in 1997 I received my PhD degree in Computer Science and Engineering from University of NevadaReno in 14 under the supervision of Dr Sergiu Dascalu

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If F(x)=x has no real solution then also F(F(x)=x has no real solutionIn probability theory and statistics, the cumulative distribution function (CDF) of a realvalued random variable, or just distribution function of , evaluated at , is the probability that will take a value less than or equal to Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an upwards continuous monotonicThis implies that there exists an element x ∈ A ∩ B with f(x) = f(x 1) Since x ∈ A and x ∈ B we have that x = x 1 and x = x 2, and hence x 1 = x 2 This shows that f is injective 3 ⇐= This breaks down into two parts itself ⊆ Let y ∈ f(A ∩ B) Then there exists x ∈ A ∩ B with f(x) = y

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