Q: f(x) * a = 49 (2n – 1)! 2". 72n + 1 + (x – 49)" n = 1 1 ㅇ윽+>m.72n+ 1.n! 1 (x - 49)" n = 0 1 1:3.5.…
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Q: dy will be dx In x+1 If y = then 2x3 - 3x' (2x- 3x) +1)- (In x+ 1)(6x? – 3) (2x – 3x)? A. (2x - 3x)…
A: To find the dy/dx of the given function
Q: The solution of the equation d'y -y=k(k = a non zero constant) dx² which vanishes when x = 0 and…
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Q: Suppose that T is to be found from the formula T=y( e*+ e-X), where x and y are found to be In 5 and…
A: GivenT = y(ex + e-x)
Q: dx 1. Evaluate e x(In x)3
A: We’ll answer the first question that is question (1) since the exact one wasn’t specified. Please…
Q: Let y : R →R be the real-valued function defined on the real line, which is the solution of the…
A: Ans:- Initial value problem: y'=-xy+x, y=0=2 solution : y'+xy=x, 40=2 is of…
Q: (- 1)"x" .n (– 1)"x2n (2n)! (– 1)"x 2n+1 V3 = = n=0 (2n + 1)! n =0 n! n = 0 is asolution for D.E
A: Note that, ∑n=0∞(-1)nxnn!=e-x∑n=0∞(-1)nx2n(2n)!=Cosx∑n=0∞(-1)nx2n+1(2n+1)!=Sinx
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: 3x 4) 4. S-001+ 6x dx = 1+e6x a. Diverges b. converges to TL 8 c. converges to It d. converges to TL…
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Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)
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Q: Find g'(3). g(x) = In(1+t) dt In(4) 6ln(10) O In(10) 3
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Q: 1. Find for y = In () (A)+ 1 3x-2 X-1 1 x-1-x2 (B) x2 - -- x-1 x (х-1) x2 x2(x-1) x-1 1 X-2 (D) (E )…
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Q: x2 dx (x– 1)3 1 In|x-1|- X-1 + C 2(x– 1)? 2 In|x-1| 1 +C 2(x – 1)2 X-1 2 In|x-1|- X-1 1 O Inlx- +C…
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Q: 4x obtain the section of the equation Ex xl with the condition u oon X4
A: Let us consider the given PDE is P(x,y,u)ux+Q(x,y,u)uy=R(x,y,u) The equation is solved as Determine…
Q: Find the linearization of y = eV1x at x = 36. (Use symbolic notation and fractions where needed.)…
A: We have to find linearisation
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: Estimate the value of E-2 (1/(n² + 4)) to within 0.1 of its exact value.
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Q: (2x+4) + 1 x² +2x- 10 dx = x² (x² + 4x +5) (2x +4) +1) dx- x² + 4x+5, Consider dx evaluate | x² + 4x…
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Q: 1) Find dy/dt for if : y = log2 (81'n 2)
A: Since you have asked multiple questions in a single request so we will be answering only first…
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: 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: Find the general solution of dy/dx = (x - 4) / (6 - 5x + x^2). O y = 2 In(x - 2) - In (x - 3) + C y…
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Q: s at x =-1 and x = 2
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Q: 0. Suppose that x is the yield to maturity with continuous compounding on a zero-coupon bond that…
A: dB =[ (?B/?x) a(x0-x) + ?B/?t + ( 1/2) (?2B/?x2) s2x2] dt + (?B/?x)sxdz Since: B= e -x(T-t) The…
Q: {in(n² +1) Im(x +4)} 19. А. В. 1 С. 1/2 D. 2 E. Divergent
A: we have to identify the given sequence is convergent or divergent
Q: Evaluate: √x(x - 5)dx Solution: √ √x(x - 5) dx = f x²(x - 5) dx by law of exponents/ = f (x² - 5x)…
A: Given problem:- ∫√x(x-5) dx
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: If 8(x) = [e²-m (21+ - dx S[e²-In (21+1) ]dt, find g(x). -2 A e-In(2x+1) 4 B (2x + 1)² 2 Ⓒ (2x + 1)²…
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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: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…
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Q: By= In(Cx-2)
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Q: 2: The necessary condition for existence of the solution of the nonlinear equation x =g (x) in…
A: For any non linear function, to find the existence of its solution between an interval there should…
Q: 2х + A A. If dx = In [g(x)| + C then x2 + 4x + 5 A = and g(x) = 2х + B В. If dx = In |g(x)| – tan¬…
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Q: Find g' (3) . g(x) : In(1+t) dt O In(10) O 6ln(10) O In(4) O 3
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Q: 12. Find the general solution using Reduction of Order: a) y"= 2ln x b) y" + y' = cos 3x
A: We have to find the general solution: y''=2lnx. Here, the value of y1 is not given.
Q: Suppose f(x) is positive, continuous, and f'(x) < 0 for all æ in [ – 8, 4], and| f(x)dx = 76 and L…
A: Concept: Mean value theorem: The mean value theorem states that if a function f is continuous over…
Q: 6. 81n V81 - 81 – x²dx 4 A. Show that B. Use (A) to evaluate In 4 (e2x – e*) /81 – (e* – 1)* dx. - -
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Q: a'(t) = -x(t – 1), x(t) = 1 on [-1,0], is given by 1(t) = E(-1)* t – (k – 1))* k! for n-1<t <n, k=0
A: As per the question we are given the following first order time varient differential equation :…
Q: If g(x) = d __*[e' - In(2t+1)]dt, find g''(x) . dx -2
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Q: (4) The general solution to (x +3)y" +5xy' - y = 0 converges at least on and is y = Co x2+ r6 +...…
A: 4. We have differential equation x2+3y''+5xy'-y=0 now take a power series y=∑n=0∞cnxn…
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: Ex: Find the solution of The e ditt evential equation xy? with yCi) =1 2xy 2 dy
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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: Find L(x). 2y – x = 3t y + a' = 3e-t x (0) = y (0) = 0 L (x): (3s+1) s? (s-2)(26+1) 3(s-1) L (x) =…
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Q: A fish population in a lake satisfies dB/dt=cB(K-B) Fish are then added at A fish per hour. Find…
A: Please check step 2 for solution
Q: Which of the following graphs is the slope field for dx 12 -3-211. s 2 13 US 111-2-/35 1112 111²-111…
A: Here we have to solve the given differential equation and plot the solution
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: 4. Find the explicit particular solution of the initial value problem give dy -уе , у(0) %3D 9 е 8x…
A: We will find the solution to the Differential equation.
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- Find the linearization of f(x)=ln(x2-3) at suitably chosen integer near X=2.1. Then use the linearization to estimate the value of f(2.1).If g(x)= ((x^2)-4)/(-x-3) and h(x)= g(x), evaluate (integral^-4 with an index of -5) h(x) dx Answer options are 1. -9 2. 6 3. 45/2 4. 3/2 5. 2Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY
- Let y : R → R be the real-valued function defined on the real line, which is the solution of the initialvalue problemy' = −xy + x, y(0) = 2.Which statements are correct?a) The problem is not uniquely solvable.b) The solution y(x) contains an exponential function.c) limx→∞ y(x) = 1d) limx→∞ y(x) = 02. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?In the function: f(x)= (3x^2)ln(x) , x>0 What are the x-coordinates of all local minima and minima in the function?