Consider the following. f(s, t) = s In(7t) + e-1.33t f(s, t) = 2 for 1sts 20 tangent line at t = 10 !3!

Q: Find dwl dt at the given value for the following functions 1) w=x+y, x= cos(?), y = sin(t), at t = 7…

A: We have to use properties of trigonometric functions.

Q: Can you explain the question step by step

A: Given: z = f (x,y) , x= e^s.cos(t) ,  y= e^s.sin(t)

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: (1) Use the trapezoidal rule and (2) Simpson's rule, with n= 10, to approxima te the integral. Round…

A: Topic : numerical methods

Q: 8.If V=k r°, and V=4 when r=2 if dr/dt =2, find dV/dt ind th

A:

Q: 2. Given that f(t) = f cos x cos(t − x) dx, fin integral.

A:

Q: in integating the function fxcos(3r) de using integration by parts, what would you choose for your…

A:

Q: 2. Suppose | 29(r)dr = 10. Using linearity properties of integrals, calculate | (g(x) + 3)dx. 3

A:

Q: dy Find at t = a where dt 1 7. у %3D = 3s + 2 and s t2 when a =1. + 4

A:

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

A:

Q: express the length of the curve as an integral but do not evaluate it. r = eθ + 1, 0 ≤ θ ≤ π/2.

A:

Q: Evaluate the line integral / (7x + 3y)dx + (2x – 8y)dy along the curve C: x = 8 cos t, y = 16 sin t…

A:

Q: The area between the curve X= t2 - 2t+1, y= In(t) and the y-axis for 1sts5 would be found by setting…

A:

Q: 4ス+S fra) = 7 +2 Contromulily of he funihim ihe fumnim Discuss The at x= 1

A:

Q: valuate the indefinite integral. 7 dt (t + 1)?

A: Given query is to eveluate the integral.

Q: Suppose that (r, y) = e-v and o(In 2, In 2) = 1. Please use the technique of linear approximation to…

A:

Q: Just use the definition L{f (t)} = ° e-st f (t) dt with 2 integrals, one for 0 1

A: Laplace transferom

Q: Evaluate the line integral / (7x + 5y)dx + (3x – 9y)dy along the - curve C: x =2 cos t, y = 4 sin t…

A:

Q: 3. If w = e3x-2y cos 4z where x = Int , y = In (t² + 1), z = t3, aw at t = 1? at what is the value…

A: Consider the following equation: w=e3x-2ycos4z Substitute x=lnt, y=lnt2+1 and z=t3 in the above…

Q: Estimate the error if cos t² is approximated by 1 integral , cos r² dt. 4! in the 2

A: We have,

Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

A:

Q: A// compute $(4+ e*) dx+ (siny + 3x*)dy Where c is closed bounded region lying in the first quarter…

A: See the attachment

Q: 6. The improper integral 1 dx converges to Vx-5 4 2 попе 1

A:

Q: Evaluate the integral: S/2 sin(4t - u) du dt

A:

Q: Suppose that a particle following the given path c(t) flies off on a tangent at t = to. Compute the…

A: Consider the path of the particle           c(t) = (2t2, t3-4t, 0) The velocity of vector is…

Q: Use Part 1 of the Fundamental Theorem of Calculus (and properties of definite integrals and the…

A: Solve the following

Q: integral f t^3 In t dt

A:

Q: dy 5. Vy -1

A:

Q: Find the total differential. z = 2x6y9 dz

A:

Q: of Let f (x,y)=tanh-1(x-y) with x=e" and y= usinh (t). Then the value of evaluated at the point dt…

A:

Q: Estimate the following definite integrals using the trapezium rule with six strips: 0.6 (a) Vx3 +1…

A: As per the company guidelines we are supposed to solve first 3 subparts of a question. Kindly post…

Q: -2 Evaluate the integral: ² ft² n s teu du ds dt

A:

Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: So S(x + 3) dy dx 3. Evaluate the double integral:

A:

Q: Evaluate the line integral (5x + 8y)dx + (3x – 5y)dy along the - curve C : x = 10 cos t, y = 20 sin…

A:

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1. Integrate f over the given interval of x, using…

A: Consider the provided question, fx=sin2x+cos4x, 0≤x≤1. We need to Integrate 'f' over the given…

Q: 3. Show that for p> 1 and r E (0, 1), the integral below converge: dt tp

A: by limit convergence test we cab prove this, we have to treat the definite integral as summation…

Q: of Let f(x,y)=tanh-1(x-y) with x=e" and y= usinh (1). Then the value of Ot (u,t) =(4,In 2) is equal…

A:

Q: is the follecing dif Mantial opuatíon Jmeo on mot Y with x>1. ey-x

A:

Q: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the 10 cos t, y in (0 <t: curve C: x =…

A: A detailed solution is given below.

Q: Suppose Fas satisfies f'cx) = fex). Prove that 3fx)sin(3x) + f'cx)cos (3x) Sfewcos(3x) dx = %3D 10

A:

Q: Compute x² In a dx both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's 3/8…

A: For the solution follow the next steps.

Q: What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the…

A: The given problem is to evaluate the line integral along the path y=x+2 from points A(0,2) and…

Q: 3 In (sec v) 2t Evaluate the integral ex dx dt dv. 00

A: Topic = Integration

Q: Determine the avarage Valve of + he Aunction fex)=Cas(z)-Sin Cx/2) PA L-2, by using The meen vaelve…

A:

Q: Find the total differential. z = 5x³y4 dz =

A: Solve the given

Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

A:

Q: Suppose y = (sq. root of) 2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt…

A: y=2x+1 Differentiating with respect to t, we get dydt=122x+1·d2x+1dt…

Q: Evaluate the integral. 10 r FIL √16 22 1 (x² + y²) 1/2 dy dx dz =

A: To evaluate the integral ∫04∫-44∫-16-x216-x21(x2+y2)12dydxdz

Q: Use the Error Bound to find the least possible value of N for which Error (SN) <1 x 10 9 in…

A: