Find f(t). ℒ−1 {s/(s+1)2}

Q: Find the value of the constant C for which the integral 3 3C dx x + 25 X + 5 converges. C =

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Q: Solve for F(s): 01

A: Given function is ft=0,      0<t<1t,        t>1             ...(1) To find: Laplace…

Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

Q: b. Find the value of V1- 0.162sin²x dx using Simpson's 1/3rd rule, taking 6 equal subintervals

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Q: -Find the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

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Q: dy 2х + ху is separable. dx y2 + 1

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Q: Find F(s). F(s) = £{t¹8e-4tz X

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Q: Let f(x) 18xe 18 %3D (a) f'(x) : (b) Solve f'(x) 0 to determine the critical values of f.

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Q: x² = 10) Evaluate the integral S dx, x > 3

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Q: d Use the chain rule to calculate f(x), if f(x) dx, dt. -x12 f(x) =

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Q: f(2) = | : t2 – 1 dt 1+ cos² (t) At what value of ¤| does the local max of f(x) occur?

A: Given that a function f(x) and we find value of x does the local maxima of f(x) occurred. We know…

Q: 2. Find frxz for f(x, y,z)= z² e³xy

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Q: Express the general solution of dy/dx = 1+ 2xy in terms of the error function erf(4) = dt.

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Q: Find f(t). ℒ−1 {e-s/(s(s+1))} f(t)=____________________+(_____________________)U(t-________)

A: Recall the following facts.

Q: 3. Let X(t) = t2W (t) – 2 f sW(s)ds, Is X(t) a martingale?

A: X(t)=t2W(t)-2∫0tsW(s)dsWe know that, X(t) is a martingale, if,EX(t+1)=X(t)

Q: find the antiderivative of the function t(x)=5/x^2

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Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvInx 2- у 3D x2+1

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Q: Find the antiderivative of f(x). f(x) = 3e6x+ sec2(x) +x3

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Q: Verify the final value theorem of f(t) =1+et[sint + cost]. O- 1 1

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Q: 3 ) Express f(t) in terms of the unit step function u(t).

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Q: The integrating factor of the non-exact DE: ydx – (x + 6y²)dy = 0 is x-2 y-2

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Q: What is the antiderivative of 1 / (x - (1/k)x^2) with respect to x? k is a constant

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Q: Find Lf 0- £{[ e-axdx } by transforming e atu(t) then applying the integratiori property

A: Given :I=∫0te-axdx Laplace Transform u(t)→ℒu(t)us=∫0∞e-stu(t)dt we need to find: ℒ∫0te-axdx

Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

Q: Q4) Use the chain rule to express dy /dx in terms of x and y t2 y = t2+1 and t = 3x3 – 3 where x =1

A: Given y=t2t2+1 and t=3x3-3 and x=1

Q: Find f(t). s(s + 1).

A: L-1[F(s−a)]=eatf(t) From first shifting property, L{e^(at)*F(t)} = f(s-a)…

Q: Find the total differential z = 5x3y2

A: The given function is z=5x3y2. Total differential: Let z=f(x,y) be continuous on an open set S. Let…

Q: The integrating factor of the non-exact DE: ydx – (x + 6y²)dy = 0 is

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Q: Find the zeYo k its ovdev for Sunction f2)=1-Ti + Z+ e.

A: Given the function, f(z)=1-πi+z+ez. Now, in order to find the zero of the function f(z), we will…

Q: If u = f(x), then f- dx ++2x+1 +C for some constant k. Compute kf(1).

A: In this question we have to compute kf(1).

Q: Q2) Evaluate the integral x3 dx 3 a *0.

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Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: Find the gradient ∇f of the function f given the differential. df=2ye^xdx+xe^xdy   ∇f=

A: Note that            . Here, df=2yexdx+xexdy. So, here we have fx(x, y) = 2yex and fy(x, y) = xex.

Q: 2. Solve the IVP 2x + y + 2xyy' = 0, with y(1) = –2. d (Hint: This ODE is neither first order…

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Q: 4- 13 + 6y = 0 dx

A: We have to be find

Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

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Q: Find the particular antiderivative of the function f(x) = e"(2" – 1) whose graph passes through the…

A: Integration

Q: b. Find the value of V1-0.162sin²x dx using Simpson's 1/3rd rule, taking 6 equal subintervals

A: We apply Simpson 1/3rd rule it is given that six sub intervals must be mentioned so in the interval…

Q: [4xy + 2x] 5) Let F(x, y) =[ 2x² + 1 Is F conservative? If so, give a potential function for F. %3D

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

Q: Find the integral +C 1 dx x² – 16

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Q: se N.P.M. to estimate the root of -X = e -X for an initial of Xo =0

A: Here f(x)=e-x-x,  x0=0. We estimate the root of f(x)=0 by using N.R.M.

Q: Find the most general antiderivative of f(x) = -10x – (1 – x²)-1/2, where -1< x < 1.

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Q: ** If g(x) = S [e* - In(2t + 1)]at , find g"(x) dx ex. (2x + 1)2 A ex – In(2x + 1) 4 ex + (2x + 1)2…

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Q: df Use integration to find f(4), if = dx O -26.667 O -19.667 O 26.667 O 30.333 5x2, and f(1) = 7.

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Q: Find an antiderivative of the function f(x)=e2x.

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Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…

Q: Calculate the error of approximation E, for: f(x) = v3x + when x = 8. Ax = dx = 0.1

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Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate: