If f(x)=3In(x)-1 and g(x)=e2, then f(g(5))=  a) 6.83 b) 12 c) 14 d) 45.98 e) 568.17

Q: Q4/ if f(x.y)=x-y and g(x.y)=3y prove V2) gVf-fVg g? %3D

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Q: Using the Convolution Theorem, what is L[h(t)]?

A: In this question, we use the convolution theorem to find the Laplace transform of the given function…

Q: Fird the inversc trons frm of ; F (5) = sz+ 25

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Q: |(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

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Q: Let f(2)= ¹5 and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of…

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Q: Show that (a) 8(at) =8(t), (b) 6(t) = 8(-t), %3D %3D la|

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: & b. su j+ byz²

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Q: tes, sno W inut E [XY] = E[X] E[Y] E [g1(X) g2(X)] = E [g1 (X)] E [g2 (X)1 and

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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: Q2: Prove that: d csc-(InVx) dx -

A: The main objective is to prove ddxcsc-1lnx=-12xlnxlnx2-1. It is known that ddxcsc-1x=-1xx2-1.

Q: OProve that (r=s)Er S is toutology?

A: The objective is to prove that r≡S≡r↔S is a tautology.

Q: Q15: Consider the D.E. (x – 1)³x²y" – 2(x – 1)xy' – 3y = 0. Is xo = 1 an ordinary point? Explain…

A: To solve the following diffrential equations

Q: The Cornev 8-I make outbound A, B. 3. achieve Ax-u38/--12A.B %3D Otrue 2)Err

A: We know that  a×b represent vector product of two vector a and b  a.b represent scalar product of…

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

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Q: P is the midpoint of GH implies that GH = 2PG.

A: We have to prove that GH=2 PG if P is the midpoint of GH. Drawing the figure of given condition, we…

Q: Find mZG. E 35-/2 F 70/2 mZG %3D Submit

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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: Using the substitution u = 2x – 1, prove that - -3 8 dx 1 (2x-1)3 25

A: The given integral is ∫13x(2x-1)3dx Put 2x-1=t⇒2dx=dt when x=1 then t=1 and when x=3 then t=5 So,…

Q: az Find for z = x'y'eV

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Q: 2) What is the relationship between 2J andOZK? K Supplementary Adjacent Vertical Complementary…

A: If sum of two angles is 90 degree. Then the angles are called complementary.

Q: 2. If LM = 10 and PS = 11, what is KN? ls 3. If PS = 2x + 4 and KN = 5x+ 2, and LM =-3x + 8, what is…

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Q: f. . Prove false by creating a counterexample: 9(AUB) C P(A) U P(B)

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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: What is G = xy ax – x²y ay + 2y az at B(3, –4, 1), expressed in SCS?

A: Given: G→=xy ax-x2y ay+2y az -----------(1) Where, Bx,y,z=B3,-4,1 --------(2)

Q: et A be 4X4r nas non-brivial . -son-

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Q: (c) Will it always be true that W C X f(W) S (X)?

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Q: One 56 Use fPicard method to approximate y when a= 2, given that y=1 when r=o and dy da

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: -3y(In x)' +3x* (In x) y' =0

A: First simplyfy the given differential equation.Then taking integral on both sides and solve it.

Q: it is unbaised estimated of a Then Show That ta is baised estimated of O2.

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Q: 1. Is the following always true? If yes, clearly explain why. If no, give a specific counterexample…

A: Note: AS per our guideline we are supposed to answer only one question. Kindly repost the other…

Q: - show that; L-1[e¬v$] = e %3D 2tynt

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Q: if y=Asinx+Bcosx then prove d2y/dx2+y=0

A: Given,

Q: evaluate using the appropriate method or combination of methods.

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Q: So So t² etu du dt

A: Given, ∫03∫0tt2etududt

Q: 7 Suppoe | f(x) dæ = 3, f(x) dx = 14, | f(æ) dæ = 7. %3D Then 8. f(x) dx Σ I F(x) dzæ = Σ

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Q: If the substitution u= J2x+| iS used, then Só V2x+ī dx is equivalent to ?

A: Substitution will be done by the given variable

Q: 2s If F (s) = (s+1)2 then

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Q: Suppose y=ect where c cannot be equal to 0. If a is a given positive real number, when does y=a?

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Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 %3D fx) =4x

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Q: If f'cx)= gica) for 0LKLH, then fca)=9(x) for OLxel True or false?

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Q: 20TH MAHH, Determine The deriva )y=3e* +916 4x t I +

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Q: Use Example 4 to calculate -(r x r'), where r(t) = {t, t2 , et)

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Q: $ Find the goneral Solutim of the differen tial equatim : (D²-60 +10)y =20-e2x

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Q: 53 what is 13' 3 Given that f(x)dx = f(v)dv?

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Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 fx) =4x

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

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Q: Evaluate the convolution between h(t)= e2u(t), and x(t)=2u(t).

A: From the above details we have,

Q: Q3) If f(x, y?) = x² + y2 + Vxy find : af(x²,y) and f(x?,y) ду

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Q: 19 When approximating / f(x) dx with 10 rectangles, what is Ax? 1.8 18 O 19 10 1.9

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.