4. Consider the IVP x' = Ax, where A = (a) Show that A = PDP-¹, where -2 -1 1 0 1 1 P = 00 -2 12 1 0 3 and and x(0) D = 0 2 0 0 (G) 2 3

Q: Option 2: Problem Solving You wish to invest P10,000 for a period of 5 years. Which of the following…

A: The principal amount we have is ₱10000 and the time period is 5 years.  Therefore,  P=₱10000 t=5

Q: Let f(t) 3t* Then f'(t) = 7t + 7e'.

A: SOLUTION-

Q: 4. Compute y' where y = 06x² - 6x 6x - 6 O4x - 3+1/2 04x-3-1/2 ONone of these 2x³ 3x²+1 x

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Q: Proldom nog y(x) Find y as frofx ly "" + 64y' = 0; y(0); y'(0) = 24; y²¹ (0) = 0 ia (32) ma 08-…

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Q: 51. y = 3x + (V3 – 5): and y = -J3x + (-/3– s)

A:

Q: ) if fcx) f (x) = = f 2 [ x² + x² +5 sin (+) dt

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: P(x) = x² - 6x³ + 14x² - 54x + 45 aun no benewens woy noltsmotni ert s2U (s) :(piaga) a + x - x - x…

A: NOTE: Refresh your page if you can't see any equations. . here constant term and leading…

Q: Compute. (a) ds/dp if s = 3( p2 + 5p + 1)10 (b) d/dt (at2 + St-1 + S2)

A: (a) We have given s=3p2+5p+110. To find dsdp we have to differentiate s=3p2+5p+110 with respect to…

Q: (4x + 1)2 x2 - 5 Find S' if s = s' =

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Q: 6. y = 5e* +3

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Q: 4. If g(t) = et +e-i' then g'(t) is which of the following? 2et + 4e2t (A) e2t + 2+ e=2t 2et + 4e2t…

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Q: 3. 2y"" − 3y" – 3y² + 2y = (e*+ex)²

A:

Q: 1. If y = In(V x² +1 ) , then y' = 2x (b): 2x (a) x² +1 3(x2 +1) () 3(x2 +1)-2/3 (d) 3(x2 +1)

A: y=lnx2+13⇒y=lnx2+113⇒y=13·lnx2+1   ∵lnxy=ylnx

Q: 5 3 ) f(x) = 4x+ x°+7x-2 Show that 4x$+ x²+7x-2 =0 has only one real rot.(Hint App!ly INT and MUT to…

A: Given,  f(x) = 4x5+x³+7x-2   This is algebraic equation, which is continuous and differentiable in…

Q: If s = (x² + 1)²/3 (3y² + 8y +4) 4(3z+2) 5, find d²s d²s dy² d²s dz²

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Q: 5 – x 3. If f(x) = , then f'(x) = x' + 2 – 4x³ + 15x² – 2 (A) (² + 2)° – 2r° + 15x² + 2 (B) 2.x³ –…

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Q: 2(x-1) + If y = Vx? – 2x then y' 3x2-2x T O F

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Q: If s = x O 9/11, 8,5/8 find . d²s dx² d²s dy 2 d²s d=² d²s dx2 d²s dx2 11 d²s - dx² 121 Click Save I…

A: Given

Q: (a) Find the approximate integral of the following function using Simpson's 1/3 rule and (b)…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Let r(t) = Find i'(t) F'(t) = < V

A: Consider r→(t)=4t4-2,3e-2t,-4 sin (5t) we have to find r→'t

Q: (-2m*)' (2a'6') (32y 13. 14. 8m (2ab*)' 15.

A:

Q: If P(A) = 0.2, P (B) = 0.4 and P (A|B)) = 0.1 Compute P(A'n B) Enter your answer with two decimal…

A: It is given that: P(A)=0.2P(B)=0.4P(A|B)=0.1 The objective is to obtain, P(A'∩B).

Q: 7.Find a²z of z = 2x³-5xy² xy

A:

Q: •1 cln(5) 1- S SmS) xy evx ´dydx r

A:

Q: Determine if the following is a fundemental set of solutions to  y'' -6y' + 25 = 0 Given that…

A: If the Wronskian of two solutions is not equal to zero, then the given set of solution is…

Q: 3. (а) U{a} x [0, 1] — (b) N{a} × [0, 1] = gER geR

A: Find the union and intersection.

Q: If f(x) =x - r- 3x+6, what are the critical value(s) of f(x)? (a) x only (b) x=3 only (c) x=-,,x=ì,…

A: Consider the given fx=23x3-52x2-3x+6

Q: 4. Find ez dz fa-1+31-8 (3² + 1)(= + 9) |z-1+j|=/

A:

Q: the work on this test need page. Pleaser 1. Integrate the following 2z3-4-8 (a)2+4 dr (b)(1-)e" dz

A: For solving this integral, first to find out partial fraction of the integrand:

Q: Find S'if S = S' = (5x + 1)2 x²-2

A: The given function is

Q: 5. Show that xZx + yZry = yezy if z= xy + y In xy

A:

Q: 4. J(2y + 3)? у+2 dy

A: Find your answer below

Q: - 7t? - 6t + 2' 7t² –1'3t³ + 7 7 7t Let r(t) = Find r'(t) F'(t)

A:

Q: Ex. 130. Given the s-domain signal: F(s) ( 7 s^2 + Determine the steady state value of f(t) using…

A: we have Fs=7s2+3s+9s3+10s2+13s limt→∞ft=lims→0sFs