Prove using the IVT. ex + In x = 0 has a solution.

Q: Evaluate the improper integral 2x dx, if it exists. (x² + 81)2

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Q: Evaluate the integral (2 + 6) (2? + 6z + 2)*dz by making the substitution u = x² + 6x + 2. + C

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Q: The DE : y'= e 5x-7y is seperable Select one: O True False

A: We have cheek

Q: Evaluate the indefinite integral. 4 dt (t + 11)? + C

A: Integration of 4/(t+11)^2.

Q: evaluate the in! integ ral if u = 16+ ex then e* V T6tex dx = ( Jü cu=(ile %3D

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Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

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Q: Show that Ě = 3xyê+G)+2Ê is R3 and Pind Conservative a potential Ø Rar F. on

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Q: Solve the Auxiliary DE 75. и"" + u" — 2и 3D 0

A: Note: - “Since you have asked multiple question, we will solve the first question for you. If you…

Q: Q53- X--) (xij-Xi - X.j+X)=Zero 13D 「に )に prove that e to

A: We need to prove the given equation.

Q: Vx4 + 39x + 13 – 4 = 0

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Q: the integrating factor of the non exact DE ydx-xdy=0 is -1/x^2,show your solution

A: We will solve the problem

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: The DE : y' = e5x-7y is seperable Select one: True False

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Q: 4 – dt 2 cos 4t 1.

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Q: Solve the equation by Cauchy's integral formula. ez dz z - 5

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

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

Q: Evaluate the improper integral 2x dx, if it exists. (x² + 81)² 8.

A: The value of the integral ∫-∞02xdxx2+812 is given by: ∫-∞02xdxx2+812=-1x2+81-∞0=-181-1-∞=-181-0=-181

Q: The approximation to a root of the equation x^2+x-1=0 in the interval [0,1] b applying the regula…

A: The given equation is x2+x-1=0  find the value of f(0) and f(1)  fx=x2+x-1f0=02+0-1=-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: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

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Q: 2h 1+h )-2 = 1 – if h<<r Prove that ( %3D r

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Q: solve the given nonhomogeneous ODE x^2y"-2xy'+2y=x^3sinx by varition of parametrs

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Q: Express in the form x + jy Q7/ (2) In(3 – j)

A: Solution:-

Q: Solve for the Bernoulli DE 2t ds = s dt + 5t4s3 dt

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Q: Evaluate the integral. 1 cos 2t dt 2 7x/2

A: To evaluate the given integral.

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: 7. Prove that if v >-1/2 ; p) = L{xvJ, (; = xı-at-a) H

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Q: sec²(3vt) dt (4) VE

A: According to the bartleby guidelines I have to solve only first question in order to get the…

Q: S 1.Prove that L (coswt) = %3D s2+w2

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

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Q: Find the general solution to the DE using the method of Variation of Parameters: у" - Зу" + Зу'…

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Q: Verify by direct substitution that Un(x,y)=sinnx sinhny is a solution of Uxx+Uyy=0 for every n&gt;0.

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Q: J sec° (10t) tan“ (10r) dt 4 10.

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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: Evaluate the integral. 2 2 t+ dt 15 OA. 29 О В. 6

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Q: The solution of integral Vu2 + u +1 du is:

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Q: Determine the general solution for following Cauchy-Euler Equatio dy + 7x +5y = x³. i) dx2

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Q: Q1 : prove 1 2(1–z) 3(1--z) dydxdz = 1

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Q: 2. Derive a formula to approximate S* s* f(x;y)dxdy yo xo Using Simpson's rule with x2 – xo = 2h ,…

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Q: the following "quation sutisfied Cauchy - Rieman equation es .4 W = Z

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: FIND THE UNTQUE SOLUTION OF AU= 0 34/x1<4 SUCH THAT U(x) 5 on x =3, U(x)=6 on /×/ =4 on 2 in R in R…

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Q: The triple integral ¹³(12xze²y²) dxdydz is equal to 3(e − 1) - True False O

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Q: 2. Use the met hod of undet er mined coefficients to solve t he syst em x' = Ax+f, where - -] b. A =…

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Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: Find u(x, t) which solves the problem Utt = 9urr -00 < x < o0, - 0 <t <3; 1 u(x, 0) = 1+ x2 Ut(x, 0)…

A: D'Alembert Solution;    u(x,t)=ux,t=12f(x+ct)+f(x-ct)+12c∫x-ctx+ctg(ξ)dξ where u(x,0)=f(x),…

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: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

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Q: Compute for the value of tanh-(1 – i) In 5 my + 2.13i In /2 + 2.13i Inv - 4.25i 2 In /2 + 2.13i

A: Let, tanh-11-i=z. Thus, solve for z:…

Q: Q2-Prove that = va* – x² ify= ()sin () + () va² - x* = va² – x* if y = (;")sin*+ (4) + () Va² - x²

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