8. Find the length of TG in the diagram below given that WG || AT, T'G = x, GC = 2, CW = x +5 and WA = 12.

Q: Given that y=e is a solulion to y" + 4y'- ky = 0 . What is the value of k?

A:

Q: 24. Evaluate x² dx + yz dy + (y²/2) dz along the line segment C joining (0, 0, 0) to (0, 3, 4).

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: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

Q: E. Prove the following: 四- Iz.l 1.

A:

Q: (c) Given tanh (x) + tanh (y) = 1, show that, dy 1- y? dx 1- x2

A:

Q: The linear approximation at r = 0 to sin(2x) is A+ Bx where A is: and where B is:

A:

Q: 7) if p(X) =- ) , and grea) =0; g'LW)=), Find f'la). %3D

A:

Q: Q Find the deriva tive using the de fini tion (x)

A:

Q: Given a level suface 4x2y2 + 5xy = 4 with y = y(x). Find! dy at the point (3, 2). Give your answer…

A: A detailed solution is given below

Q: Solve the diferential egyatien dy - by Melne's méthool with h-o-1 e Cosx dx

A: GIVEN: y'=e-xcosx-y   The formula is: yn+1,p=yn-3+4h32yn-2'-yn-1'+2yn'    ............(1) Put n=3,…

Q: Given that y'= 3y - 100t and y(0) = 10, estimate y(1) using delta t= 0.01.

A:

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

A: Solve by double differentiation

Q: ue of the det e 16 is

A:

Q: Use Euler's method to obtain a four-decimal following: approximation for t (4 y=2Xy, yC)=1; yU5) =?…

A:

Q: If y = xsin then y is equal to = X" at x =

A:

Q: - If x=sect and y = tan t, evaluate at t of the following: 4. dy (a) dx d y (b) dx?

A:

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

A: The complete solution is in given below

Q: Solve the difterentiol equatten by method of Uudetermined colefficients 27 ty't 4y= S -e'te

A:

Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

A:

Q: Consider the figure below. uestion 1 T. 2x W Зх - 5 Previous

A: Given TW= 2x, 3x-5

Q: If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = || N, = X, Since M,…

A:

Q: 2. for, (x+y)X = tan-14x + TT* + dx dy a)- Find InIny

A:

Q: 10 q/ asing the TracZoidal Rue with n= dx Swbintevals, evalute the in tey ral I+2 and compare as…

A: Find the attachment

Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

Q: Given that: z = y sin(2x) + (1+x²)e* + cos x tan¬1(y* + 1) In(y6 + 137)

A: z=ysin2x+1+x2ex+cosxtan-1y4+1lny6+137 Differentiating wrt x, we have…

Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: 0.6158 0.6165 None of…

A:

Q: Gren thint sin (A+i6) = xtiy, 28 Prove that, 9父+ =1 snh'B 1) x essec?A -y' sec'A =1

A:

Q: 1 Find 는 dx by using chain rule, if f = u + u = T x , at x = = 4 cos?u

A:

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: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

A: A line integral is the integral of a function along a curve. The function can be scalar-valued or…

Q: 2) Show that La- (1 – x²)P',(x)P'm(x) dx : 21(1 + 1) Sim. 21 +1

A:

Q: Given f(x,y,z) = sin (2xy) + 5xyz3. Find fyzy(3,2,4).

A:

Q: 16. Find he exact soution on The interval [0,2m] 25in?x ャ Bsinx +3= 0 5sinx t

A:

Q: -8. AB is tangent to to OC at point B. E 6. MZCDA - 8. MZDBA = 32

A:

Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x 1+ x²

A: Answer is mentioned below

Q: 3ey , find Given z = dz dz au

A:

Q: 2, If fCx)=xInCx²+), find the ea uation for t4e tan9ent 1ine to fCx) at x= 3.Hint: Remember the…

A:

Q: Evaluate: / (In(2r – 1) – () + 25) da + 25 ) dx | Limits: [1, 6] Using Trapezoidal, n = 30

A:

Q: The linear approximation to fix) = E at x = 8 is given by O a. 2 - x Ob. 2 Od. 12

A: Given: f(x)= x3 Linear approximation of a function fx is given by the formula  y=fa+f'ax-a

Q: (1) If Euler's method is used to approximate y(t), the local truncation error, Ti+1 is defined as…

A:

Q: Find the value(s) of @ for which y = cos ot satisfies d'y + 16y = 0. di? Enter your answers in…

A:

Q: dy 13. y(1) = e de ar(In y - Inr + 1)'

A:

Q: 6. If x= sect and y=tant, evaluate at t =- of the following: dy (a) dx d'y (b) dx?

A: x = sect y = tant

Q: 6., Given that= 1' + sy = ) and that y = 1 dr (a) show that for values of r close to 0, 1 when = 0,…

A: Let y(x) is a function. Then the expansion of Taylor series of the function y(x) at the point x=a…

Q: The linear approximation at and where B is: = = 0 to sin(9x) is A + Bx where A is:

A:

Q: 2 Without using technology, sketch the graphs of the following for 0°<x < 360 a y = sin æ + 1 90 180…

A:

Q: (c) Given tanh (x)+ tanh¯'(y) =1, show that, dy 1- y? dx 1- x2

A: The given function is: tanh-1(x)+tanh-1(y)=1

Q: (4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u…

A: