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Q: Suppose that f(0) = 1, ƒ(0.5) : 2.5, f(1) = 2, and f(0.25) = f(0.75) = a. Find a if the Composite…

A: Given:           x         0         0.25      0.5       0.75        1      f(x)     1        α…

Q: 10 X =1.2 is to be sol he initial approxima

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Q: 2) vting daplace toansfóöre, Solve x" Zt)+4x'Lt)+3=(4) uing = 10 gint yeren that xco) = -3t Ans: ILt…

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Q: 4. 5 Show that if y%= x+4 then dx (x+4)** %3D %3D 16. dx. 2 (x+4)² **n Hence, find the value of|

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Q: TQ residue of f(z) = e (z – 1) (z + 9) at z = -9 is 10e-9 :Select one True False

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Q: Q2: Using Theorem 3, find f(1) if L(F) equals: 1 28. (s + V2)(s - V3)

A: Given, LF=1s+2s-3 To find the function ft.

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: The evaluation of S z dx is V4+x2 O In(sece + tan0) + c o - In(sec0 + tan0) + c c In|sece – tan0|+ c…

A: we have to evaluate the following integral .

Q: 4. Ifu = f(x), then : dx = J x* + 2x² + 1 k + C for some constant k. x² + 1 Compute kf (1). (a) ¼…

A: The given integral is ∫xx4+2x2+1dx=∫xx2+12dx To compute kf1

Q: Use Secant method to to approximate the solution of f(r) = z+ cos z =0 accurate to within 10-3,…

A: The secant method is used to calculate the root of the function. The formula for the secant method…

Q: Expand x?y + 3y – 2 in powers of x + 1 and y – 2. (up to third degree terms).

A: Given :- The given expansion x2y + 3y-2 in powers of x+1 and y-2.

Q: Prove that in the pairs of positive numbers ¤, y for æ² + y° = r the sum a+y is greatest when z = y.…

A: Here we solve the given problem of calculus.

Q: The function def ined by y=Acos(In(x)) +Bsin(In(x)) d²y dy is the solution of the following DE: x²-…

A: True . i.e. the function defined by y=Acos(ln(x))+Bsin(ln(x)) is the solution of the differential…

Q: of (x)} = h %3D a Find leughth

A: Length=integration of  square root of 1+(f'(x)) 2

Q: O we N. P.M. to estimate the root of -X for on initial guess of Xo

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Q: Prove that P(X = n) = 1. 00 %3D

A: Given that  We have to proof that  ∑nP(X=n) =1

Q: 3. Show that the following ODE is homogeneous then solve it. 2xyy' = x2 + y?

A: 3). Given: 2xyy'=x2+y2 So, we can also write as: 2xydydx=x2+y2dydx=x2+y22xy....1 Let,…

Q: -2 Let f(t,y) = y + 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1<t<2.…

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Q: In(1+2x) Find the Padé approximation R1,2(x) for f(r) %3D

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Q: In ΔFGH,  FH is extended through point H to point I, m∠FGH=(x−2)∘,  m∠GHI=(4x−5)∘, m∠HFG=(x+19)∘.…

A: Given that     FGH is triangle. FH is extended through point H to point I .

Q: S 1.Prove that L (coswt): %| s2 +w2

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Q: The largest interval for which the IVP : (In(e* – e²)) y' + y = 1, y(5) = 0 х —6 has a unique…

A: We need to find the largest interval for which the given IVP has the unique solution.

Q: The largest interval for which the IVP: (In(e* – e)) y' + y = 1, y(5) = 0 %3D X-6 has a unique…

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Q: 2 (b) S(2 + tan (0))do (c) S 2'(1 + 5')dt

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Q: a) Prove If he Given DE Is exact or non-exact Find its General solution

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Q: The value of c of fo-2- in the iterval .D such that rio--E) OA 3 OB. -3 OC 3 O0. 3-

A: c = 3explanation is given in below step

Q: Ex:- Min Z= X-3 X2-2 X3 %3D sub to 3X1 - X2 + 2 X3<7 -2 X + 4X2 く12 -4Xi+ 3X2+8X3 slo Find anew…

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Q: Find the largest interval on which the LV.P (x +(4) x -5) y" + sin(x) y' + y =0, y(0)= 3, y'(0)=4…

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Q: 7- f (x)= 3.x², 0<xr<1 olarak verilsin. P(/2/ (2, = ? O a. 1/8 O b. 1/4 Oc 3/4 O d. 7/9 O e. 1/9

A: Solution: 7. From the given information, the probability density function of X is

Q: If k> 0 such that k S x 8k dx = 7 then

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Q: Integrate f(x) = 0.5 + 20x + 3x4 from a=0 to b=3, given N=12 by using a) Simpson's 3/8 approximation

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Q: 7. a) Prove that for r > 0 * (E) + c. Vr2 – r²dx = vr² – x² + -1 sin 2 +C.

A: To prove: ∫r2-x2dx=x2r2-x2+r22sin-1xr+C

Q: 1 f f(x) = : R → R, Vx2 – 4 At how many different integer points x is discontinuous? 25 - O A) 3 O…

A: We have f(x) = 1x2-4Clearly f(x) assumes real values for all real values for all x except for the…

Q: 1(3x-5)dA;R is a Triangular Regian- bounded by 7. ¥=DX+5 %3D Eval& ReverSc ?

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Q: at to a o and terms of power senes' and opa apen n nlervas f Converganca dt t t. 2.

A: Given The given integral is ft=∫t1+t4dt Taylor series for fx=1+x+x2+x3+···=∑n=0∞xn, where x&lt;1. If…

Q: En=1" Vn sin а. 1 b. 2 c. Converge

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Q: メpr t! prove that : d = (s«k-tank)

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Q: We hae a theorem that offers conditions when the IVP: x'- f(t, x), x(to) = X , has a unique…

A: See the attachment

Q: 2 2 2 1+ 2 t3十 Cn)和 9 Prove that

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Q: ind positive numbers x and y satisfying the equation xy=21 such that the sum 3x+y is as small as…

A: GIVEN DATA : Positive number x &amp; y satisfying equation xy=21 and the sum 3x+y is small.…

Q: F(x) = | VE? + 11 dt 5 Let Find (a) F(5) – | (b) | F'(5) = (c) F"(5) –

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Q: (2? + y? + 1) dæ – (æy+ y)dy= 0 - %3D x +1 (x + 1)? Option 1 Option 2 (x + 1)-3 (x + 1)-1 O Option 3…

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Q: Which of the following is Inx – 6x + 18| + arctan(- (x – 3)) +C equal to? 2 – 6x + 18 x - 3 V 2 In…

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Q: 3) Find the general solution by using reduction of order method to ty" – (t + 1)y' + y = 0 given…

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Q: 6., Given that= 1' + sy = ) and that y = 1 dr (a) show that for values of r close to 0, 1 when = 0,…

A: Let y(x) is a function. Then the expansion of Taylor series of the function y(x) at the point x=a…

Q: Given G(x) = jin(2t+1)dt , find G '(x). O In(2x + 1) O In(2x + 1) - In3 O In(2t + 1) + C 2 2x+1

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Q: 0. For what values of a and b is ax + 2b, 8(x) x² + 3a – b, 0 2 tinuou s at eiery r'

A: Follow next step