1. r(t) = ti + (In cos t)j, -T/2 < t < T/2
Q: 6) Use Laplace transforms to solve the differential equation: d²y dy -72+10y=e2* +20, given that…
A:
Q: Show that y(t) =t-2 ln t is a solution to ty"+5ty' +4y 0. (where t> 0)
A:
Q: 2) 1 y = ²+² x= cos(t). y = sin² (t).= =-. at t = 3 t
A: Solution of the given problem is below...
Q: 33. Find a linear differential operator (of lowest order) that annihilates the given function: f (x)…
A:
Q: 2) Obtain the DE with respect to x of (x - h)² = 4(y-k).
A: Sol
Q: (b) Solve the integral [(3x – y)dx +(2x +3y)dy along the curve x = y' from (0,0) to (1, 1).
A: Solution of question as follows
Q: Prove that sinh−1 t = ln(t + √t2 + 1 ).
A:
Q: d²x dx + 2 * + 5x = e-t sin t; dt [ = x(0) = 0 x'(0) = 1 %3D dt2
A:
Q: 10. Use differentials to estimate to estimate sin(46°). vZ(n+180) А. D. VZ(T+180) 360 180 В.…
A: Let y = sin (x)
Q: Solve the initial - value problem : dy = Cos x - Sinx +y, 0 sx < 0.5 , y(0) = 0 dx using (a) four-th…
A: Given differential equation dydx=cosx-sinx+y,…
Q: The differential equation 3zy" – 2y + 7y = tan x is normal on any open interval not containing = 0.
A: The main objective is to determine the given statement is true or false.
Q: 1/2 2. Approximate the integral: 1 - cos(2x) dx within an error of 0.01. x2
A: According to question given that∫0121-cos2xx2dx within an error of 0.01
Q: b) Suppose x # 2. Find dif dx In y = In (x - 2)² √x² +1
A:
Q: 6) Use Laplace transforms to solve the differential equation: dy dx2 dy -7- ·+10y=e2* +20, given…
A:
Q: 1.5 3-y Q1) Evaluate the integral dx dy
A: To evaluate the given integral.
Q: 9-20 Compute the differential dz or dw of the function. 17. w = x'y?z
A: Given
Q: 1.1 the integral f cos(lnx) dx . x2 1.2 the integral S x³V1– 2x dx
A: 1.1 Given integral is ∫coslnxx2dx Let u=lnx⇒dudx=1x dx=xdu1x=e-u∫e-ucosudu we will integrate by…
Q: g(x) = 2x−7+4 2x-π+4 o TT/2 sin² x g(t) dt
A:
Q: In Exercises 28-34, find ƒx , ƒy , and ƒz .
A:
Q: () 2. If k = w3 – wv², w=xy, v = w+ x, find and using: dw a) the chain rule b) differentials.
A: Given: k=w3-wv2, w=xy, v=w+x To find: (∂k∂w)x . (∂k∂x)w using chain rule and differentials
Q: 4 2 1 Evaluate || - dy dx by reversing the order of the integration. O V Y +1
A: Given:∫04∫x21y3+1dydx
Q: 1 Let y = -. Find dy and Ay at.x = 7 with dx = Ax = - 1. Enter the exact answers. dy = Ay =
A:
Q: (4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1
A: As per the Guidelines, I will answer the first 3 Integrals. For the fourth one please repost the…
Q: Prove: ex. a. ſ csch x = In b. S sech x = 2 Arctan(e*) + c
A: a). ∫cschx dx=∫2ex-e-x dx=∫2ex-1ex dx=∫2exex2-1 dx Put, ex=t⇒ex=dtdx⇒ex dx=dt Therefore, ∫cschx…
Q: 8. Evaluate the double integral. cos 2x.sin y dy dx
A: Solution-
Q: sin(2t + ) dt e21-3 4 7 4 4 64e 7
A:
Q: In 3 by Pots tien 3) S (4 - x)e"'dx calculate without integre (f Ju
A: Given,
Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||
A: Partially differentiate with respect to x and y by using product rule.
Q: 1. Evaluate the integral: (a) cos(x) dx dy 4y
A: the given integral is: we have to evaluate the given integral.
Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)
A: Please see the answer below.
Q: dy 1- Solve = cos x + y, where y = dx 2.0 at x 0 take step size h = Ax=
A: Given, dydx=cosx+y Where y=2.0 at x=0 and h=0.1
Q: 4) (2x + y cos xy) dx t x cOs xy dy - o cOs xy) dx t X COS Xy dy COS
A:
Q: In (6x) to x if y = sin (5e') dt.
A:
Q: 8. When reduced to a linear DE of order one in z, bernoulli' equation dy/dx +y (1/x) =3x2y2
A:
Q: 1. -ay + A sin dy 2 = Br, dt
A:
Q: tanh (22) d) evalvare J seen 2 (2n ) e レッ using a substitution Suitable
A: To evaluate the given integral.
Q: 26. Let y= Væ. a. Find the differential dy. b. Evaluate dy and Ay if æ = 1 and dx = Ax
A: a) Given that , To find :…
Q: 8) Let z = y-x². Use differentials to estimate dz when x = 1,y = 5, dx = 0.03, and dy 0.1. !! %3D
A:
Q: 3. Find dy/dx of the followings: (а) у | V2 + cos³ t dt 2. •7x2 (Ъ) у V2 + cos³ t dt 2 (c) Y 1 dt t2…
A: using fundamental theorem of calculus part 1 ddx(∫abf(t)dt)=f(b)ddx(b)-f(a)ddx(a)
Q: 1. Show that x = sin (Int) is a solution of t2: (5) 0 = x +1+.
A:
Q: Compute the general antiderivative S a"-1 cos(x")dx COS where n > 1 is an integer greater than 1.
A:
Q: 1.) 201 4sin (x) cos (x) dx dy 0 y² + 1 [¹ylnª (y² + 1)
A:
Q: 7. (cos x+xcost)dt +(sin t -t sin x)dx = 0 Ans. t cos x+x sint c 8. (ysin x+xy cos x)dx +(xsin…
A:
Q: Prove that the general solution of the differential equation √√1+cos(t) d0=(√1 + cos(t) — t sin(t)…
A:
Q: THE IVP
A: Consider the provided differential equation with initial condition is,
Q: 4. Express the integral e-t tổ dt in terms of gamma function.
A:
Q: Q: If In/x2 +y2 =sec(), use implicit differential to proof the following: - dy (²+y*). sec?. tan?…
A: lnx2+y2=secyx
Q: d²x + cos(t)- dx sin(t)- + sin(t)x = tan(t) dt dt2 x(1.25) = 6 dx = 5 dt 1.25 has a unique solution…
A: The differential equation d2ydt2+ptdydt+qty =rt .......1 with conditions yt0=y0,…
Q: (b) Solve the integral (3x– y)dx+(2x+3y)dy along the curve x = y' from (0,0) to (1, 1).
A:
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
- Find the lengths of the curves in Exercises 25–27. 25. x = cos t, y = t + sin t, 0 <=t<= pai 26. x = t3, y = 3t2/2, 0<=t <=sqrt(3) 27. x = t2/2, y = (2t + 1)^(3/2)/3, 0 <=t<= 4You are now allowed to assume that the half-planes determined by the line with the equation ax+by +c = 0 correspond to the points (x, y) so that ax + by + c < 0 and ax + by + c > 0, respectively. Usingthis, show that axiom B4(i) holds. (Hint. Suppose (q, r) and (s, t) are on the same side of the given lineand that (s, t) and (u, v) are on the same side of the given line. en construct the parametrized linethrough (q, r) and (u, v). Consider the mappingλ γ7→ a(q − qλ + uλ) + b(r − rλ + vλ) + c and note that it is continuous and either increasing or decreasing. Use this fact to show that, for everyλ, γ(λ) > 0 or γ(λ) < 0, depending on which half-plane the points are on.)Suppose that z is an implicit function of x and y in a neighborhood of the point P = (1, 1, 0) of the surface S of the equation: xy + yz + zx = 1 An equation for the line tangent to the surface S at the point P, in the direction of the vector w = (1, −2), corresponds to: The answers are in the attached image.
- Find T, N, and k for the plane curves in Exercises 1–4. 1. r(t) = t i + (ln cos t)j, -pai/2<t<pai/2 2. r(t) = (ln sec t)i + t j, -pai/2<t<pai/2 3. r(t) = (2t + 3)i + (5 - t2 )j 4. r(t) = (cos t + t sin t)i + (sin t - t cos t)j, t >0Consider the curve C in R3 whose parameterization is given by: eq. in image If is there a point on C P( 3/2, 1/2, √2) A vector tangent to C in P corresponds to options in imageFind the lengths of the curves in Exercises 19–22. 19. y = x^(1/2) - (1/3)x^(3/2), 1<= x <=4 20. x = y^(2/3), 1<=y<= 8 21. y = x2 - (ln x)/8, 1<=x <=2 22. x = (y3/12) + (1/y), 1<= y<=2.
- Sketch the plane curve r(t) = a cos3 ti + a sin3 tj and find its length over the given interval [0, 2π] .1. Chapter 15 Review 13: Sketch the domain D (in the xy-plane) and calculate sDf(x,y)dA.D = {0 ≤y ≤1, 0.5y2 ≤x ≤y2}, f(x,y) = ye1+xIn Exercises 5–8, r(t) is the position of a particle in the xy-plane at time t. Find an equation in x and y whose graph is the path of the particle. Then find the particle’s velocity and acceleration vectors at the given value of t.
- Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds to (-2, 0)In Exercises 11–12, find an equation for the plane that is tangent to the given surface at the given point. 11. z = ln (x2 + y2 ), (1, 0, 0) 12. z = e^-(x2+y2), (0, 0, 1)In Exercises 11–12, find an equation for the plane that is tangent to the given surface at the given point. 11. z = sqrt(y - x), (1, 2, 1) 12. z = 4x2 + y2, (1, 1,5)