∫(5e5√y/√y)dy That is 5e to the (y to the 1/5)

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y * logy x *

A:

Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: Given a6x CosT+Sy - .3x. -Siny+ 10x-e -*, defermine (1) T'=S(T) ax T'-

A: Given:T"=6x2y3-cosx+5y2-siny+10x2-e-3xTo determine:i  T'=∫T"dxii  T'=∫T"dy

Q: Q2. Show that dx ax + by di dy = cx + dy di can be written as + yx = 0

A: The given system of differential equation is. dxdt=ax+by                     ......1dydt=cx+dy…

Q: ven f(x,y) = -2xy² where x = 5t and y = 8t2. Findf' (t) at t = 3. %3D

A:

Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

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: ential equati x²y dy = C

A:

Q: Dy + y Prove that is equivalent to 1 for x 0. 16x

A:

Q: Use the trapezoid rule withn=4 to estimate dx . Answer must be in fraction.

A:

Q: 3. dx using n = 10 subintervals %3D 25. -2

A:

Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

Q: Find the absolute maxlimum of frr.y)=xy subject to the Coustraint glxy)= x²ty²=/

A:

Q: y +6 dy (Int. of Rational func.) y? + y` 2)

A:

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: Tind dʻz of z- In (xy) Find d²z z - In (xy)

A:

Q: What is the difference between dy dy and Ay Use an example y = 4x?+ eX to under stand. 4x2+ ex

A: In the given questioin we have to tell about the difference between dydx,∂y∂x and ∆y∆x. first we…

Q: The approximation of 1 = f(x - 1)ex² dx by composite Trapezoidal rule with n = 4 is: 15.4505 -5.1941…

A: Given  I=∫02x-1ex2dx and n=4

Q: (y5 – x²e») dx dy -11-3

A:

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

A: Trapezoidal rule:   where

Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

A:

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: Q2\ find y' when y = Vx² • sin2x + cosh 5x %3D

A: This question is taken from the derivative in which we have to find the derivative of the given…

Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: 1 Evaluate the improper intergal | dx (x2 + 9)° using the residue theorem.

A:

Q: 2. Find an expression for dy/dx on the curve x In(y) + x³ – 2y = 6.

A:

Q: Evaluate the integral. dx (х — 9)(х — 18) (Use symbolic notation and fractions where needed. Use C…

A:

Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

A:

Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: Find the derivVative of the function. 5. y= In 8v +5 dy dv %3D

A: The objective is to find the derivative of the function.

Q: 9-10 Use the Midpoint Rule with n = 4 to approximate the integral. 9. 2² dx

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: dx J x2-4x+5

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y * logy x |

A:

Q: 12. Find frxyz for f (x, y, z) = sin (3x + yz)

A:

Q: 1. Use the delta method, 2 BONUS MARKS y = 5x² dy dx = lim h-0 f(x+h)-f(x) h to find dx for the…

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Q: Compute dx using the techniques as presented in class and in our textbook. Show all 2x +5x-3 the…

A: we first factor the denominator

Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

A:

Q: - 3+ In x 3+ In x dy show that dx 2. (i) Given that y = [2] x(3 + In x)? 12 (ii) Hence evaluate dx .…

A: (i) Given : y=-3+ln(x)3+lnx Therefore, taking derivative both sides w.r.t x :…

Q: 1 The approximation of dx by the composite Trapezoidal Rule with n= 2 is +4 O X-

A:

Q: Q3: Find lim,- (2 – sin –) إجابتك :Q4 For (3x³ – 5x) V2x+1 find dy/dx at x=0 إجابتك

A: Explanation of the solution is given below...

Q: tanh (22) d) evalvare J seen 2 (2n ) e レッ using a substitution Suitable

A: To evaluate the given integral.

Q: find the dy リ=(メ+z)mx, (xを when 3In X

A:

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: dy Find for x=secy dx A xsinx B D 1-x?

A:

Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

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: If we have to check the DE (5-8y+4xy)dx = (x+2)²dy for Exact then My

A: M dx + N dy =0