*xsin-'xdx The antiderivative of is x-V1-x2 sin-!x+C A True (B) False

Q: 19-x Evaluate ,* sin(x + y*) dy dx

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Q: dx x.In5 (x)

A: Given integral is, ∫1xln5xdx. Apply substitution method: u=lnx, then du=1x. ∫1xln5xdx=∫1u5du=∫ u-5du

Q: b) I =f- x(1+(In x))

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Q: Consider the generating functions a(z) = 1 + 2z+3z² +42³ +52 + = Σ(i+1)zi = i20 b(z) = 1+z+z²+z³…

A: We have to find a formula for the coefficient of zk in  (ab)(z), where  a(z) =…

Q: 3. Determine a and b for Y X1 and Y2aX bX2 such that EX1 EX2}= 0, Var(X) Var(X2) Var(Yi) Var(2) 1,…

A: The provided information is:

Q: sVx? + 1d: Idx = 1

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Q: The function re* sin(8x) is annihilated by the operator

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Q: Differentiate y = VIn x 2 Inx +1 A. 2(In x)2 3. Inx-1 3 (In x)2 2 Inx-1 C. 2(In x)2 13 1. D. 3) 2(In…

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Q: 8F OF OF 1. Use the formulas above to find and ду ax exy + sin (xyz) + In (yz) = 4 – z

A: Partially differentiate the function with respect to x.…

Q: xsin ax 2 2 (x²-x²) 1/2 Show that [²= - dx - TV J₁ (ay) 2

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Q: -cosh(2x² + 1). Evaluate (A) 4xsinh(2x² + 1) B 2xsinh(2x²+1) C) xsinh(2x2 +1) с D (2x2 + 1)sinh(2x +…

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Q: Use an appropriate substitution to integrate 2. A sin u +c 12r'sin (x?– 2) +c © 12sin (x2- 2) +c…

A: To evaluate the given integral.

Q: (10y+11)dy 4y2 -4y+5

A: The given integral is, ∫10y+114y2-4y+5dy First, complete the square in the denominator as follows:…

Q: (즐). Using the substitution t= tan the integral dx sin(x) – 90 cos(x) can be written as dt 45 t2…

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Q: Vr+2+Vx-2 If a = prove that a -ax +1=0 Vx+2-Vx-2

A: To prove , we need to simplify the left hand side of the equation till it becomes 0. To do this…

Q: Show that - if W= cos (メ+y)+ Sin(メ-y) Wメメ Wyy ニ

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Q: What is y' of y= 7√x 3√x ? A B C D 21√³ (In 7 + ln 3) (In 4) 21√x √x 21√ In 10 2√x 3 In ( - ) 21 V ²…

A: We have to find the point on paraboa y=-x2+4 whose tangent line is parallel with y=3x+5Parallel line…

Q: cancer u alcurate 5th on diagnostic test is 9s 2 those who halse A 'cancer cnd on those wno do not

A: Given that, As the test is 95% accurate for both who have cancer and who don’t, therefore the…

Q: dy If y = 9sin x then dx (a) (cosx) 9sin x (b) (In 9)9 sin x (c) 9sin x (d) (In 9)(cosx) 9sin x

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Q: Evaluate L{3(sin² 2t )} 24 24 24s 24 а) s(s² + 4) b) d) s(s² + 16) s(s² + 16) s(s² – 16) a O Option…

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Q: Evaluate | sin(In t) dt. t sin(In t) – t cos (In t) -t sin(In t) – t cos (In t) . . 2 2 O Option 1…

A: Substitute u=ln(t) ⟶ du/dt=1/t dt = tdu t = eu ∫ eusinudu we use integration by parts ∫fg′=fg−∫f′g f…

Q: ху • prove that x +y Example If z = az dz + y.- Əx х. ду

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Q: 5 [x²² sec (2) com ³ (2) abr dx 7 2tan can ²2 ( 1 ) [7tan² ( 1 ) +1 + C (Α 77 11 7 2x + (-) == ² (7)…

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Q: ΔΙΗ ΔΚΗ by SSS Κ Η

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Q: Z= x³+y¹+(x sin y)+ (y cos x),Zx/Zy= (3x²+ sin y-y sin x)/(4y+ xcos y -cos x) O True O False

A: Given Z=x3+y4+(x siny)+(y cosx)To find ZxZy:

Q: Verify the identity. sin(x) + cos(x) = sin(x) cos(x) sec(x) + csc(x) sin(x) + cos(x) sec(x) + csc(x)…

A: sinx+cosxsecx+cscx=sinxcosx

Q: Evaluate the integrals. T [ise ²+3 •)[(**)** b) dx (8) a) c) S √√3 ~/mm 8 1 + X following definite 3…

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Q: EX~U(0,1) if Y= =L l(t-x)~ Exporential (A,

A: From the given information, X~U0,1 The probability density function for X is, f(x)=11-0       =1,…