Σ Suppose that ax" converges to a function y such that y" – 2y' + y = 0 where y(0) = 0 and y'(0) = 1. Find a formula that relates a, + 2, a, + 1, and a, n = 0 Compute a, ag. , - 1 1 a, = 1 az = 2! 1 a4 = 3! 1 as = 4!

Q: 13. If f(x) = 1 / (5 + 7x) , find S f(x) by using a u-substitution. Show the u-substitutions.

A: Given, fx = 15 +7x  We have to find ∫fx using u substitution

Q: x if x20 If Ax) = -x2 then f'(0) if x <0

A: Given function, fx=x2      if x≥0-x2   if x&lt;0

Q: If f(-1) = 4 and f'(x) ≤ 5 for all x, what is the largest possible value of f(6)?

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Q: If f"(x) = t"(x) for 0 &lt; x &lt; 1, then f(x) − t(x) for 0 &lt; x &lt; 1.

A: It is given that f''(t)=t''(x) for 0&lt;x&lt;1. It is known that derivative and integration are…

Q: Q3. Solve in terms of Bessel's function, the ODE: x²y" + xy' +((inx)² +) y =0 z=lnx using a Rule…

A: Here, x2y''+xy'+lnx2+14y=0,  z=lnx.

Q: Suppose that f is an odd function; i.e., f(-x)=-f(x) for all x. Suppose that f'(xo) exists. Which of…

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Q: Start with an initial guess x = a₁. Then define a2 to be the x-intercept of the tangent of f(x) at…

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Q: A function f has f(25) = 22, f (25) = 2 and f" (x) < 0, for x ≥ 25. Which of the following are…

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Q: Suppose that f (0) = 2 and f'(x) 0. Show that f(4) 0.

A: f(0)=2   and f'(x)≤3  for all x&gt;0 ⋯(i)integrate (i) w.r.to x ,we getf(x)≤3x+kput…

Q: Determine if = 5₁° f(x) dx is convergent or divergent when G 1 x² and find its value if convergent.…

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Q: If 69 + 5 f(x) + 2x²(f(x))³ = 0 and f(1) = -3, find f'(1). f'(1) =

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Q: 7. If f(x)=√(1-1²)et² dt, on which interval is f decreasing?

A:

Q: Suppose, f'(x)=2cosx+ sec x, -7<x<7½, and it is known that f(T) =D4. Find the function f(x). IT

A: Integrating on both sides, we get

Q: If f(3) 9 and f'(x) ≥ 2 for 3≤ x ≤ 8, how small can f(8) possibly be? f(8) ≥

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Q: (a) Use the definition of L{·} to determine L{te=#}

A:

Q: If f(4) = 3 and f '(x) ≥ 3 for 4 ≤ x ≤ 7, how small can f(7) possibly be?

A: We have to find the smallest value of f(7)

Q: 3. If f(1)=10 and f'(x) ≥ 3 for all 1 ≤ x ≤ 5, how small can f(5) possible be?

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Q: If f(2) = 5 and f'(x) ≥ 2 for 2 ≤ x ≤ 6, how small can f(6) possibly be? f(6) ► 20 X

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Q: Q1-) Determine whether the following functions are convergent or divergent: 1 1- En=1 ((3n-1)*/…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

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Q: The function f(r) = In(xª + 4x² + 3) is decreasing on Question 4. the interval(s) a) (0, 0) b)…

A: Given function is fx=lnx4+4x2+3. We have to find the decreasing interval. Decreasing function: Let…

Q: By= In(Cx-2)

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Q: Let X ~ T(a, B). If E(X) = aß and E(X²) = aß² + a² ß². If â = X, find the method of B moments…

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Q: x) such that f"(x)=2r' +3x-4

A: Integration: f''(x)=2x3+3x2-4x+5; f0=2, f1=0 ∫xndx=xn+1n+1+c

Q: 03: Let S(x)=12-x-1|-1. -1. Find f"(0) and Find f'(4)

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Q: 7. Find the intervals of increasing/decreasing for the function f(x) = x'e*

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Q: 1. 9. -2 a. Given p(x) = f³(x). Find p '(3) b. Given h(x) =f(g(x)), find h'(3)

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Q: 2/Solve the following sequence X(n)= n. "u(-n) by using the differentiation property of the…

A: As per the question we are given the following sequence : X(n) = n (1/9)-n u(-n) And we have to find…