If b is dviisible by a (a|b) and b in different than 0 then |a| is less or equal than |b|

Q: dx , if we let u =V 25 – x² , then udu = - xdx. (A True B False

A: Given query is to find statement is true or false.

Q: 00 fcos(x*) dx = ! Ex. 41. Prove that 2 V2 0.

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Q: 14. Consider that * Sof (x)dx = 2 and f'(1) = 3. Find Soxf"(x)dx. %3D 3 O 5 O 1 O 4 O 2

A: We have to find

Q: 2 sinºe cos³e de= 60 a O 120 b O 1 .c O 60 .d O 120

A: We have to solve given problem:

Q: a Prove that < 16 – a| for each a, b e R. - V62 + 1 Va? + 1

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Q: Suppose p is true, q is true, r is true, s is false. Then (-pvs) v (SAr) is T/F? A) True

A: Given : Suppose p is true, q is true, r is true, s is false.

Q: 1-y² L In (r* + y? +

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: If f(x) = exp(-x).In(x), then , when x=1, df/dx is 1/e C 2/e O e nonexistent O

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Give an e xam Ple of (T, m') ameasurable SPa ce F; x → T {E & CX : fCE) ET3 m is not

A: Given, Τ, m a mesurable space fi:X→Τ , m=E⊆X: f(E)∈Τm is not a σ-algebra on X.

Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

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Q: af Given f(x, y) = In(6x² + 8y²) then %3D

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Q: Q4 If f(x, y) = In(x² + y² ) %3D Prove that dy2

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Q: d Prove that (x") = n x"-1 dx

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Q: b? – a? x dx 9. - Proof Prove that 2 a

A: This can be proved using Fundamental theorem of calculus. The second part of the theorem is used.…

Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: a)-What is fof g ofh 3)? fari= gal= bprove f:R¬R fer )=4lis not Surgective and is not injective.

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Q: 19. f' "'In rdr r'In r dr

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Q: af Given f(x, y) = In(7x² + 9y²) then

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Q: S Prove that L(cos 3t) : %3D (s2+9)

A: We know that Lf(t) = ∫0∞e-stf(t) dt Then Lcos 3t = ∫0∞e-st cos 3t dt                             (1)…

Q: Show that F(n fla)] ds pleae do it frast

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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: Let f(2)=³ and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of Ac…

A: Given that             fz=z4-5z2      and    C=z∈ℂ : z=1.

Q: How do I prove this?

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Q: 2) Prove that: d? L„0) = n;(n – 1) %3D dx²

A: Consider the given information: Let Laguerre polynomial is given by, Lnx=∑k=0n(-1)kk!nkxk…

Q: (a) Suppose x E Q with x # 0 and y E R – Q. Show that their product ry is irrational.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Prove Va e Z, Vb e Z, 3|(a² + b² ) – 3|a ^ 3|b where xy means x divides y, i.e., there exists k e Z,…

A: In this question we use congruence modulo.The following  are useful in this question1) If  3 |…

Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: Sm Vx dx

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Q: Let H(x) be an antiderivative of 1sm z if H(5) = 7, then H(2) =

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Q: Show that os fj ex* +en+ 22n+1 + (2n+1)n! 25 e*(22n+3) dx – |2 + ... 5(2!) (n+1)!

A: The given integral is ∫02ex2dx. Using Taylor series, the exponential function can be written as:…

Q: 3. If z = f (x, y), where x = e“ – e® and y = e® – e", show that UTM UTM az az UTM X : az - ду dx…

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Q: 27 dr = iex+ h where a, b> 0. Prove that

A: Prove that , ∫-∞∞e2xae3x+bdx=2π33a23b13

Q: 3 1-Vy dy 2 2у3

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 28. (a) Prove that for x e R" and s < t, Ds(x) C D;(x).

A: The notation Dsx represent  an open ball of radius s, centered at x∈ℝn. Let x=x1, x2, …, xn,…

Q: prove that 16 x (I+x) dx 306

A: The product rule of integration states that∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx.

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

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Q: Prove that dv du 2 – u? + v² 18

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Q: Prove that jer² √ d dx = 2

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Q: Consider the formula A = Vx Vy.p(x,y) ^ ¬q(x, y). (b) Show that A is falsifiable (i.e. not valid) by…

A: We are given a formula as : A≡∀x∀y.p(x,y)∧¬q(x,y) We need to show that A is falsifiable by giving an…

Q: Q(x) = √3/2+² Ser fet de Prove that & QQ (-∞ ) = 1

A: Here we can use Gamma function formula Γn = ∫0∞ xn-1 e-x dx to evaluate the given improper integral.…

Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

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Q: В. .3 x³ In(x) + C 3

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Q: 4x³ – 3x dx 2x2 + 5 x4 –

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Q: Given that z = f (u,v), u=x + y and v = 2x - 2y. Show that 4. дхду ди?

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Q: Vx Sn(l+x*) de 23/2

A: Using the substitution ... Explanation of the solution is given below...

Q: EXs Prove that [* Ju cx) = x'Jv-1 (x)

A: This is a problem of Bessel's function.

Q: (a) Prove that if f e C (R²) then a (af af %3D

A: This is a problem of the calculus of several variables, higher dimensional calculus.

Q: for a>0 is defined a n(x² + a²) and sin ax = (x)"6 prove that la * fb = fa+b and ga * 8b =gmin (a,b)

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Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

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Q: Then show that N(A) = R(AT)+ and N(AT) = R(A)+. %3D 11-1 02-3 -1 1-2 N(A) = N(AT) =

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