If f(z) = In (z + 4 + e3=) then f(0) is А-2/5 В 1/4 C. 1/5 D the value does not exist E. none of the above Option 6

Q: Suppose that the function y(x) = E Cnx" solves the initial value problem n=0 y" (x) – xy'(x) – y(x)…

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Q: Which of the followings solve the initial value problem 2(2xy + 4y – 5)dx + (x + 2)²dy = 0, y(-1) =…

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Q: f(x) = ao + a,x + azx² + azx³ € R[x] polinomu için –2 e R, f(x) polinomunun bir kökü ise x+2 e R[x]…

A: As ℝ is a ring of real numbers. So ℝ[x] is the polynomial ring that contains all polynomials in x…

Q: 7. Minimize c = s+ 3t + u subject to 5s - t + v > 1,000 2,000 s + t > 500 s 2 0, t > 0, u > 0, v >…

A: For simplification : s = x1 t = x2 u = x3 v = x4 Let c = Z Z = s + 3t + u = x1 + 3x2 + x3

Q: Evaluate the given function (e2x – 1)dx = (e2x + 3)(ev – y°)dy is equal to.. 3y°+1 A.- e +1 x+3ev -…

A: We need to solve the given differential equation.

Q: 19) * (xy)* = e ; f ind y' y' = [1+ In(xy)I y' = -y [1+ In Option 2 O Option 4 y' = [1- In(x None of…

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Q: If x¨ + x˙ − 6x = e ^−t, with x (0) = x˙ (0) = 0, what is X (s)?

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Q: A chemical supply company currently has in stock 100-lb of a certain chemical, which it sells to…

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Q: 1. ( ) If ƒ e C[0, 5] then So So F(x)f(4)dydx = L f(x)dr|

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Q: the initial value problem y' -4t/y, y(0) on exists depends on the initial value yo. Yo, and…

A: Given :-  The given initial value problem y' = -4ty   , y0 =y0 and the interval in which the…

Q: 5. (5 – x)² * 6 Show that if y=3-x then %3D 6. . (x-s) _ xp 1. dx. 3 Hence, find the value of , 2(5…

A: In differentiation use quotient rule In integration use substitution

Q: ду h. ax if cosh(3x²y) = x + In(e*y + 1) i. If fx se and fxx arz find fyyxxx if f = x³y² – – Y əx…

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Q: The function h(x) given by h(x) = –6 – 8.2944x - 4/5x + 3.84x³ has a critical number c = = -1.2.

A: We have given function hx=-6-8.2944x-45x5+3.84x3 and critical number c=-1.2

Q: If L{f(t)} = F(s) 3(s+3) and f(0.5) is s2+6s+8 e + 1 e2 (). given by K( : then find the value of K

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Q: In +1- 2 dt, if we let V Vt+1-2, then dt is equal to t+1– 2, then dt is equal to A) None 4x³dx ©…

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Q: For z > 0, 옮(1 In (t³ + 1) dt A) In (x³ + 1) B) In (8z³ + 1) c) 2 In (z³ + 1) 2 In (z² + 1) D) 2 In…

A: Solution: Consider the given that; ddx∫02xlnt3+1dt We have Leibnitz Rule: ddx∫a(x)b(x)f(x,t)dt =…

Q: A radioactive sample decays according to the law - -hy where k>0 Suppose c represents the size of…

A: From the given differential equation:   dydt=-ky   So, dy=-kydt...Integrating on both…

Q: If z + In(e3* - e + e²) = 0 dz find at the point (0, 0) -3 -2 3. 2.

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Q: For ſ k*e3* dx = 1 (ke)3x 3 (1–In 2-1) + C. If u = 3x, then k =?

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Q: cos (2t + ) dt e21-3 -3 e 4 64e3 7 e-3 4 7 e3 4

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Q: (6) Let x1, -- ,X1o N(u, o2), where µ e R and o > 0 are unknown parameters. Consider the following…

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Q: kx 4+x² If k > 1, evaluate O ka -In|x² + 4 +C 2 Okx -arctan (2x) + C 2 Ok In(x² + 4) + C O arctan…

A: Given: I=∫kx4+x2dx   ...1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

Q: 1 F(s) %3D 2 s+1 s+3 (s+2) 6 F(s) = e-s (s² +4).

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Q: Find the Solution (1+r)ds + 2sr-3(1+r)dt = 0; when t - 0, s = 2. ® : (1 - P12-e* ®= (1 - s12-e © : =…

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Q: 3. f(x) = -x² +1 Ex)(+x). x2 + x - 6 %3D Holes: Vert. Asy: Hor. Asy:

A: Now plotting the graph of given function we get :

Q: Use the theorem of Leibniz in the following problems: If y=x³e2x find y(m) and hence y(3). julm) =…

A: Leibniz rule states that (f(x)⋅g(x))n=∑r=0n Cr nf(n−r)(x)⋅gr(x) Let fx=e2x and gx=x3

Q: 2) Suppose A is a constant such that Ae2a is a solution to the DE y' + 4y + 3y = e2a. Find the…

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Q: d [e'- In (21+1)]dt, find g(x) . dx -2 A ex-In(2x+1) 2 B ex_ (2x + 1)2 4 C (2x + 1)² 4 D (2x + 1)²…

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Q: e. y= (x² + 4)/x in the interval 1<x<4. 8+ 4ln4 - % s.u ans.

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Q: 1. Expand x³y²(x + y)12. E15.(15) xn+3y15-n ,15-п а. n 12 b. Eo () xn+3y14–n ELo (5) xn+3y14-n С.…

A: From the given information. The given expression is .

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: An insurer has data on losses for four policyholders for 7 years. The loss from the ™ policyholder…

A: Given  r=4,  n=7 ∑i=14∑j=17Xij-X¯i2=33.60 ∑i=14X¯i-X¯2=3.30

Q: 1 d) 2r- dz - r e² – e-z e) J ez +e-z° rp- In 3 f) 1 ez +e-z Ip-

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Q: 25x g(x) = In(3 + V7 ) dt Find g'(8) (A) In(43) – In(3 + V4 ) (B) - In(43) – In(3 + V4) 2Vs (C)…

A: We have to find the integral

Q: 2.4.10 Show that det(e4) = etr(A) for all A E Mn(C). D %3D

A: The given problem is to show the given identity. To show: det(eA)=etr(A) for all A belongs to Mn(C).

Q: L %3D e2t e-3s-6 (s+2)? O e6-3s ( 1 3 + S+2 (s+2)2 O e-3s (s+2)2 1 3 s+2 O e2-3* ( +) 1 (s+2)2 s+2 O…

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Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

Q: Evaluate the given function (e²x – 1)dx = (e2* + 3)(e" – yº)dy is equal to. 3y°+1 = x + 3e –…

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Q: d If g(x)=- S* [e²-In (21+1) ]dt, find g(x). -2 2 (2x + 1)2 4 B (2x + 1)² Ⓒe-In(2x+1) 4 (2x + 1)² di…

A: A function is given by, gx=ddx∫-2xet-ln2t+1dt. The objective is to find the second derivative g''x…

Q: S f(x) = x² – 2x + 6 x > 1 x4 + 2.x3 + 2 x <1 Show that there c E (-2,3) such that f(c) = 4. (Don't…

A: topic - continuity and limits

Q: The general solution to the D.E. xey'- e = x2 ,x > 0 is y = In (x² In (x) + cx?) y = In (x) + cx2 y…

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Q: 1. If L{f(t)} = F(s) then L{f""(t)} is, A) s²F(s)-sf (0) - f'(0) s²F(s)-sf'(0)-f(0) B) C) D)…

A: Topic = Laplace transform As per guidelines , At a time only one question can be answered out of…

Q: 1. Find the particular solution of the DE: y' = (x^3) + e^(10x) + 7 if y = 20.1 when x - 0. You may…

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Q: 1. g(n) = n² + 5 f(n) = 3n + 5 find g(n) ÷ f(n) 2. g(a) = −2a + 5 f(a) = 3a + 5 Find (g/f) a 3.…

A: Given (1) g(n) =n2+5f(n) = 3n +5g(n) ÷f(n) = g(n)f(n)= n2+53n+5

Q: If we use a linear approximation of e- at a = 0 to approximate e-1/3, then we obtain: А. 4/3. В. 2/3…

A: The solution is given below

Q: One of the critical points of f(x,y) = x³ – 5y² + 10y – 27x is: O (1,-1) O (3,1) O (3,-1) None of…

A: Necessary Condition for Critical Point: A necessary condition for x, y to be a critical point of the…

Q: Given that n2 1 and xn =V 4n² + 3n – 2n Will {Xn}, be divergent or convergent? n=1 Will E-1 Xn be…

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Q: Given y" + 2y' + y = 3t*e^(-t) whent = 0, x = 4 and x' = 2. Solve for its solution Y(s). a. Y(s) =…

A: we have to solve for Y(s).

Q: 1 al 1z(z -4)e – 4)e z=1

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Q: Suppose f( – 1) = – 8 and f'( – 1) = 7. Find the following. E (7z² – 10z – 6) S(z) at z = - 1 is…

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