*18. (section 3.4 ex 3.) Prove that if f(r) is continuous and f(z) = S() dt, then f(x) is identically zero. rtins 2E 1 N Dewo the formnlo.

Q: dt converges. There is no value of r such that (3t)-" 14.

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Q: 8. Theorem 1.7.4 x -le* dx is convergent if and only if n > 0.

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Q: 1 (x + 1)2 dx -2

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Q: Example: Examine the convergence of COs x dx (ii) / x'e*² dx

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Q: 3.2= e'-ry ; I=t3 and y = t° %3D

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Q: 4. Let A(x) = ſ dt. Find the local minima, local maxima, and t2+1 inflection points of A(x).

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Q: 1+e-* Show that dr diverges.

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Q: Suppose that for each i such that 1 <i<N one has / f(1)dt = i Ji-1 What is / f(t)dt if N = 87?

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Q: Section 3.7: 1. Consider the integral: de (r - 1)2 (a) Use integration with a limit to show that…

A: We need to use fundamental theorem of Calculus.

Q: Find the absolute maximum and absolute minimumvalues of  f on the given interval.

A: Given equation is Differentiating both sides, we get Now, we will wind critical points of f(t) in…

Q: 2. If :|S1, determine the maximum modulus f(:) (a) f(=) =z-2z+3, (b) f(=) == +z-1, (c) f(=)3= :+1…

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Q: 3. (a) Show all functions satisfying u"(x) = 0 are linear by integrating the expression of u"(x) %3D…

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Q: the Following is divergent

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Q: If f (x) is an invertible, differentiable function with tangent line y = 4 x + 7 at the point (0, 7)…

A: we have to swap variable for finding the inverse function

Q: Solve the initial-value problem for x as a function of t. da = 3, x(2) = 0 (2 - 242 +t - 1) %3D %3D…

A: Given initial value problem is,

Q: (c) f(x,u, v) = – log(uv - x" x) on dom f = {(x,u, v) | uv > x² x, u, v > 0}.

A: C.

Q: X1, ., Xn are idd. find the MLE and cramer rao lower bound for unbiased estimator for theta. f (x |…

A: Given  fxθ=θ              when x=-11-θ2θx     for x=0, 1, 2, ....

Q: (a) Show that the moment generating function of X is given by 1 Мx() - 1<t< 1. 1 – t2

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Q: 3[ .. :] Let X and Y have joint pdf S 2x, 0<x< 1,0 <y<1 0, f(x,y) = otherwise Find the covariance of…

A: Cov(X,Y)= ?

Q: Section 3.4-The product rule and Quotient Questions In(x) Differentiate: y = Q1 Q 2 (0 Q 3 ( Q4 ( dy…

A: To find: The differentiate y=ln xx7. Concept used: Quotient rule of differentiation.…

Q: 4. Let (X,Y) be distributed with joint pdf ·[1 + xy(x² − y²)] if |x| ≤ 1, [y] ≤ 1, f(x, y) = - £1¹+²…

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Q: 1/x e 7 dx y3 -1

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Q: 2. Suppose the PDF of X is given by fx(x) = 5e-5x(o)(x). Find its CDF.

A: Solution

Q: Example 2.3.16 Determine the following integrals are convergent or divergent 8 for e-2x dx

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Q: f fn → ƒ uniformly and the functions fn have only jump discon- sinuities, prove that f has only jump…

A: Here we use epsilon delta proof

Q: If f is a continuous function on [0, ∞0) and | f(x)dx converges, then I f(x)dx diverges. 3 Select…

A: Given that, f is a continuous function on [0,∞). And, ∫3∞f(x)dx  converges. Then,…

Q: Discuss the Convergence or Divergence for D { [4+ (-0"]" (Z+2)" こう 2n+1 - DZ² 2 لع Wi ngo (2n+¹)!

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Q: Part (b) 7s +4 Find L-{F(s)} (s + 4)° Let F (s) = s2 + 4

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Q: (a) Show whether if 0<x <1, f(x) = 2 - x if 1<x < 2 is a Dirichlet function.

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Q: (Section 17.3, 17.5) Consider F(a, y) = (e-" cos(y))i + (e-" sin(y))} (a) Show that F is…

A: Here is the solution of the given problem. Line integral:  Conservative Vector Field:

Q: Example 1.7.3 Prove that dx/x is divergent. 1

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Q: Determine if the given is convergent or divergent. (x²+1)² n Zn=1 (n²+1)²

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Q: sin(²) En=1 is 18 √n a. 1 b. 12/12 c. Converge d. Diverge d O C O a O b O

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Q: Suppose that F(u) denotes the DFT of the sequence of f(x)={1, 2, 3, 4}? What is the value of F(14)?…

A: Given: F(u) denotes the Discrete Fourier Transform of the sequence f(x) = {1, 2, 3, 4} To find F(14)

Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

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Q: 2 Q/if the function fc)=ĕ is not Continuous at T where =TIL x<T foint the fourier Scries of fcxeě is…

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Q: Theorem 1.7.2 [ x-'(1– x)" -dx is convergent if and only if m > 0 and n> 0. Scanned with CamScanner

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Q: 11. Show that the Beta function, defined by B(x,y) = (1-t"-1 dt , for x> 0, y > 0, satisfies the…

A: the given function is βx,y=∫01tx-11-ty-1dt for x&gt;0,y&gt;0 substitute t=1-s therefore, dt=-ds when…

Q: Let X, Y ~ N(0, 1) be independent. Find the moment generating function of X2 + Y2. Hint: If X, Y…

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Q: -5 1 10) Determine whether the improper integral diverges or converges: ī dx Vx-1

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Q: If E, 2"an converges and Eo(-1)"2"an diverges, then the radius of conver- gence of Eo anx" is 2. =0

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Q: Solve the DEQ given the initial condition (4,-2). Graph it on the slope field. 10 9 1 8- Let…

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Q: 1 [3] b) Determine whether dx converges or diverges. Justify your answer 1+x?

A: According to the question, we have to determine whether ∫0∞11+x2 dx converges or diverges. If the…

Q: 3. Find upper bound for error of linearization of the following function at given point Po(1,2), 4.…

A: We can solve this by using partial derivative formula

Q: 6. (Section 4.3) Find the area under each curve over the indicated interval. (a)y = 6- x2, (-2, 1]…

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Q: Suppose f and g are continuous functions. Provide an example such that | g(x)dr diverges 0. adf(x)dr…

A: Follow next step

Q: メー) whatis theradius h.gh of convergense f the power senes) 9.3 b. 2

A: ∑n=1∞(x-1)nn.3nwe have to find radius of convergence of the power series

Q: 5. Show that |Logz|<|In(z)|+ t, for all z # 0.

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Q: 5.2-9. Determine the constant c such that f(x) cx (1 – x)°, 0 < x < 1, is a pdf. |-

A: Given: fx=cx3×1-x6        0&lt;x&lt;1

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.