Demonstrate the Calculus 3 formula f Ss V1+ 2² + 2; dxdy

Q: Evaluate ff, x² In(y + 1) dA where R = [0,1] x [0,1].

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Q: Use the Second Fundamental Theorem of calculus to evaluate J (6x2 + Jdx. You get: O A. 10 В. 52 О с.…

A: we have, ∫136x2+6x2dx The anti-derivative of 6x2 is 6x33=2x2, and the anti derivative of 6x2 is…

Q: d by f(z) = (x alytic, then C %3D

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Q: c) 59 ² + √x dx x

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Q: 49. x = f(p) = 950 – 2p – 0.1p - - (A) p = 30 (B) p 50 (C) p = 70 %3D %3D

A: We will use the price demand equation at find the demand is elastic . unit elastic or…

Q: The domain of F(x, y) =x*y+ x*+ = 1 D =R²- {(0, -)} A O D=R BO D=R? .C O D=R-{}

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Q: True or false? As x→∞, x = O(2x)

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Q: Use the one sided Greens function to solve the I.VP. -1 2 In 12, y(1) =0, y'(1)=1 412 y" +8ty' + y =…

A: Given equation is, For solving homogenous equation, By cauchy euler equation,

Q: Generate the approximation formula 1 f'(x) × - [4f(x+ h) – 3f(x) – f(x+2h)] 2h with the error term.

A: The objective is to generate the approximation formula,

Q: Find the value of a so that V1-x² O 1 2 O 3 2

A: SOLUTION-

Q: True or false: x=5 is a counterexample to the statement (Vx>0)(x-x 0). O True O False

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: adra a. EX XXX + 3) c. 2(X + 3) -2 0. -3

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Q: If S f(t)dt : 3x2 + 12x, what are the possible values of a? Verify that your values of a are…

A: The given integral relation is: ∫axf(t)dt=3x2+12x From the fundamental theorem of calculus,…

Q: 3. Use the Argument Principle to show that (a) f(z) = z + 1 has one zero in the first quadrant, and

A: Given: f(z)=z5+1

Q: A) Eliminate the arbitrary constant/s: 1) 2x³y + xy? 40 %3D

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Q: If h(x) = V6 + 5f(x), where f(2) = 6 and f '(2) = 3, find h'(2). %3D h'(2) = %3D

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Q: Describe the long run behavíor of f(r) = r° – 3r° – 2rª + 5 %3D - -

A: The long-run behaviour of a function is the behaviour of the function at its endpoints of the…

Q: Prove that F (3.x)(A → B) → (Vx)A → (3x)B. 3.

A: To prove: ⊢∃xA→B→∀xA→∃xB

Q: Show that Q) J2(x)= J0(x)+2J′′ 0 (x).

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Q: Let f(x) = cx4.2 and suppose that f(5) = 30. Find the value of c.

A: Given f(x) = cx4.2

Q: x" – x" + 4x' - 4x = 20Cos(21) x(t) = ? =>

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Q: There does not exist r E Q ə r² = 2 ylgn ihi

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Q: 4. Determine whether the following statements are True or False? y = f(x)

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Q: Find f") if Aa) - (V 1)(x* - 1). %3D O a) -4 O b) 4 c) d) 1

A: Solve the following

Q: Show if z = 2 + 4i satisfies z? – 4z + 20 = 0

A: To show that a value or number satisfies an equation, we substitute the value in the equation and…

Q: If f(x) = x² + 3, then ƒ(x + h) =? Select one: a. x² + 2xh+h² + 3 O b. x² + 3 + h² c. O d. x² +3 + h…

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Q: Jx-6dx is 3(x-6)% -+c 2 Ob. (x-6) +c O . (x-6)% 2 O d. 2(x-6)% -+c 3

A: I=∫x-6 dx   Let x-6=t⇒d(x-6)=dt⇒dx=dt

Q: Q1. Given x+x=0, please prove that x +x = x. %3D

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Q: 2) 1 V1-x² dx

A: The given integral,      ∫11-x2dx

Q: Find x E R that satisfies -2 , – 02 + 2 vz U2 det = x det + – ö4 2 0 + 03 U3

A: The key concept to solve the given problem is that : The determinant of a matrix remains unchanged…

Q: 13. -(р — q) -рл-а 14. (р — q) л(р — г) %3D р — (q л г) 15. (р — г) л (q - г) %3 (pvq) — r

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Q: Find the constants c0, c1, and x1 so that the quadrature formula Z 1 0 f(x)dx = c0f(0) + c1f(x1),…

A: Consider the given quadrature formula, ∫01fxdx=c0f0+c1fx1 here we need to determine the constants…

Q: If Sf(x)dx= cotx? +C, then f(x) is equal to A -2cscx2 В none of these © -2xcsc?x2

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Q: Use substitution method to prove step-by-step that (P^Q)^(P = ¬(Q^R))^(S = R) = –¬S.

A: We are asked to prove the following using the substitution method, P∧Q∧P⇒~Q∧R∧S⇒R⇒~S We will show…

Q: Verify that af ?x || 224 ?х ду = 224 ду дх - for f(x, y) = 7x®y³ – 5x5y4.

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Q: Evaluate F· dī where C F = = , and C is given by - T(t) = , 0 < t < T 0 <t<

A: Given

Q: Let a,b be constants, a 0. If Y = aX +b, show that p(X, Y) = lif a > 0 p(X,Y) = –1 if a < 0

A: It is given that Y = aX + b We have to calculate the correlation coefficient between the variables X…

Q: Given that F′=f, use the substitution method to show that ∫f(ax+b) dx=1aF(ax+b)+C, for nonzero…

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Q: (c) Find A? fo given that fo = 79, f1 = 120, f2 = 150, f3 = 190, f4 = 201, f5 = 218, fe = 250, f7 =…

A: We will find out the required value.

Q: If f(x) = 2x' - 2/x+4ln x, then f' (1)= %3D О а. 9 O b. 8 О с. 11 O d. 10

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Q: Show that || Ar +b|3 cTx +d f(x) = {x |c"x +d > 0}, where A E RmXn, bE Rm, c€ R" and d e R.

A: As per the instruction, we will be solving part (b) of 3.23. We are given the function…

Q: Let f(x) = cx -1.28 and suppose that f(6) = 29. Find the value of c

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Q: f(x)=x+1 is O(1) True False

A: We have to state whether the following statement is true or false. f(x) = x+1 is O(1).

Q: B) Write the formula for (f o g o h), f(x) = vx +1 , g(x) = h(x) = = x+4'

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Q: Let d: R2 × R2 →R given by

A: A metric space is a pair (M,d), where M is a set and d is a function M×M→R satisfying the following…

Q: ppose that x + 6 f(x) = _d f'(2). 2) = %3D

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Q: Find the given value. Ax) = 1 – x?, r"(-v2) "(-v2) = f(x

A: Differentiate the function fx with respect to x to calculate the first derivative of the function.…

Q: Irr( V1 + 7, Q) = Vī, Q) = O gt – 4x² – 2 O xt – x - None O xt – 2x² – 6

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Q: If S. f(t)dt = 3x² + 12x, what are the possible values of a? Verify that your values of a are…

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Q: Find f'(x), f"(x), and f3) (x) for f(x) = - 5x? +4. .... %3D f"(x) =D

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!