b) Find L{e™t f (t – e)H (t – e)} |

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: dz/dy for z = e^xy

A:

Q: Find dy/dæ in terms of t if x =t – t°, y = 2+ 4t dy/dx =

A: The differentiation of parametric form of functions can be done by using the formula,

Q: A) Use the chain rule to find where w'sy',x= sint + cost y = cost - sint. B) If f(x. y) - xy?+ x'y ,…

A:

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: Given: y=7x-1 We know that ddxxn=nxn-1                                                       ..1

Q: Show that E [x(t)] = 0. %3D

A:

Q: Q9/ use the chain rule to express dy/dx in terms of x and y and choose correct answer. 1 x = t2 at t…

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Q: (c) Prove that L{Cost Si(t)- Sint Ci(t)} Logs s +1 %D

A: The complete solution is in given below

Q: dy/dt= 2e-t/8, t is greater than or equal to 0

A:

Q: ;(y+ 1) e*dx = (e* + 1)y dy, what is F = 1.F. J (-e*y - y)dy? %3D

A: Given: y+1exdx=ex+1ydy

Q: Find dy if x=t+6f and y= dx 2 5 at t=1 +

A: We have to find dy/dx

Q: Q1-If x= cot- VE, y =, find d²y dx' dx2 at t = 2.

A:

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

A: Recall the following facts.

Q: Find aw/as and ôw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) X = s + t, y…

A: we have to find partial derivative by using chain rule

Q: Q3) Find dy/dt of the function y = cos (5sin (t/3))

A:

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: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: 3) Find dz dy for z = e

A: Solution: As per given date   z=exy  For finding dz/dy , we assume that 'x' is a constant.

Q: 39. f(a + 1+2 tag z + tag' x) dx = S (sec" z + 2 tag 2) dz tag z)' dz %3D tag z + 2 In Isec z| + C

A:

Q: b) Calculate dx for n = 6, using Trapezoidal rule. 1+x5

A: Trapezoidal rule:   where

Q: w = In(x²+y² +z²) x = cost y = sint z = 4E

A: w=lnx2+y2+z2, where x=cost, y=sint, and z=4t. Find dwdt.

Q: 3) f(t)=t cosh(at) Ans. F(s)= s' + a? %3D 5) f(t)= 2te' Ans. F(s)= (s-1) %D 2.

A: We find Laplace transform of given function

Q: E(x)三ㄧ-rx.VY.tmdt. Į nd Eicx) Let

A: Since f(t)=sqrt (4-t^2) is even function , so we use the property of definite integral shown on…

Q: (e) dy if y = (t +1)(t + 9) %3D dt It%3D3

A: Given that y=(t2+1)(t+9)

Q: + y = e In t 16. 2y" + 2y' + y = 4Vx 17 3x" 6y' + 6y = e* sec r

A:

Q: i f(t) is given E ue of f(0.5) is

A:

Q: 크(F(a+) e dt dx 19

A: We have to evaluate, ddxFx4=ddx∫10x4  e-t2 dt

Q: Obtain dy from the following function y= e v*

A:

Q: Ex2: Solve by using Laplace transform y'-x = et • x'+y = e=t, where, x = 0, y = 0,

A: The given system is, where initial condition is x=0, y=0. Now taking Laplace transform of equation…

Q: Hw z] Find Sxsin(x)dx using this rule.

A: Given that, Using the chain rule, The integral becomes,

Q: 1) f(t) =t cos(@t) 2) f(t)=tsin(@t) 3) f(t) =t cosh(at)

A:

Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

Q: 2. Find dy where y = v3x3 +4x + 1.

A: Given y=3x3+4x+1

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

A:

Q: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find

A:

Q: Express in form y=f(x) by eleminating the parameter x = ln t , y = 2 − t

A:

Q: E x² t xY +y'l find the velue Ot yll at Pint where t=\

A:

Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: Evaluate: L{t f -t e2t Cos t dt}.

A: Evaluate: Lt∫0te2t costtdt First of all we find    L(cost)=ss2+1L(e2tcost) =…

Q: Find In(y') at the point (0, 1/e) where xy° – In(xª + y) = 1.

A:

Q: Evaluate dt dW at t=0 for the function W = e' – In x , x = t², y= In t

A:

Q: se the Chain Rule to find dw/dt. w = INVX2 + y2 + z² x = 9 sin(t

A: Here we have to use the chain rule to find dwdt=? w=lnx2+y2+z2, x=9sin(t), y=3cos(t), z=5tan(t)

Q: aw nd dt in term of t, if w = xy, x = cost and y = sint, when t = - %3D

A: Question 4 is not complete.  I am answering Question 5.

Q: If a = 5+ti and y = 3t - t then dy at t = 1 dz is :

A: as per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: What is the I.F of dy/dx=(y+y^2)/x?

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Q: Verify the linear approximation at ( 0, 0) for e^x cos(xy)

A:

Q: 3. For x= In /t y=t2, find y'-y"when x=0.

A: To find: The value of y'-y" when x=0 . Given: The value of function are x=ln(t) and y=t2. Formula…

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx + x²dy by the curve y y = x2.

A:

Q: 3. Given the graph of x' vs x, sketch the direction field for x(t) that corresponds. dx dt

A: Use the graph to draw the direction field. Observe how the graph passes through the visible points…