(d) S (1, y) = sin (2), (x, y) # (0,0) 0, (x, y) = (0,0) (e) , r + y # 0 7+y x² + y = 0 0, f (x, y) =

Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

A:

Q: If f(x, y) = y° cos(x) – x³ In(y), find the second partial derivative ду дх .A ² f ду дх 3x2 -2y…

A: Calculate partial derivatives

Q: 81 fx, y) dy dx 10 10 O-10 10 1아 1아 -10 10 -10 -10 81 -x F(x, y) dy dx = f(x, y) dx dy

A: we have to change the limit of integration.

Q: If f(x, y, z) = 16xy – 4yz – 4zx + 3, then the first order partial derivative fz = - - (4y + 4x) - –…

A: When a function is differentiated concerning a particular variable and the rest all the variables…

Q: Can i get help step by step please

A:

Q: 29, + 16y=0 geoJ = 2, go)= -2 2. 31, dy dy -54 =0 dt

A:

Q: If x2 + y2 = 25 and dx/dt = -2, then what is dy/dt when x = 3and y = -4?

A: Given x2+y2=25Differentiating with respect to t,ddtx2+y2=ddt25

Q: 15. cos y sin 2x dx + (cos2 y cos²x) dy = 0. cos² x(1 + sin y) = cos y(y + c - cos v). ANS.

A:

Q: dy : y4 — e²xy³ = 2 sin(x + 3y). dx cos(x+3y) + y²e2xy³ 2y³ +3[cos(x+3y) + xy²e²xy3] cos(x+3y) +…

A:

Q: b. Find for each system. dx x = – sin(3t) х— —1 + 2 cos t х 3D 4 cos y = cos(3t) y = 4 + 2 sint y =…

A:

Q: 2 xy dy – (r' + 2y³) dx = 0 xsin 2 dy y sin- -x | dx

A: Homogenous differential equation: Let us consider differential equation of the form…

Q: 7,9,-4) y dx +x dy +3 dz = (5,4,1)

A:

Q: 2.Find the particular solution of y (9x-2y) dx -x (6x-y) dy=0., when x=1, y=1. Let x=vy

A: Find out the particular solution.

Q: 4. (y² cos x - 3x²y – 2x) dx + (2y sin x – x³ + Iny) dy when x = 0, y = e %3D 5. (x² – 1) dy = ((1 +…

A:

Q: (3) Integrate using an appropriate substitution 2e- -d.xc e + 3 x-

A:

Q: If f(x, y) = y cos(x) – a° In(y), find the second partial derivative ду дх .A 3x2 = -2y sin(x) ду дх…

A: Option (a) is correct.

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sec-1 (x + yz)

A: Given that f(x, y, z)=sec-1(x+yz)

Q: find dy/dx

A: y=∫sec x21t2+1dt.

Q: 2 In sec Vi + tag V + C sec sec z dz %D

A: 35. given integral,∫sec x . dxx = 2∫sec x12 . 12x-12dxlet x12 = u⇒ 12x12-1 dx = du⇒12x-12dx = du

Q: (4,0,2) S sin y cos x dx + cos y sin x dy + 3 dz (1,0,0)

A:

Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

A:

Q: 2(1-z) Evaluate S-" ==-2) dy dx dz

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: -2x + 3x -x) dr- (sin y + y e (y e + +3y e) dy 0. x(0) 1 D 2r-- O 2y - y+ xr e O x+ 2x-y e-3y e+3e–…

A: The given differential equation is,(y2e-2x+3x2-x)dx-(siny+ye-2x+3yey)dy=0, x(0)=1

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

A:

Q: 4. (y² cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e

A: exact differential equation

Q: If  x2 + y2 + z2 = 9,   dx dt = 3,  and  dy dt = 5,  find  dz dt when  (x, y, z) = (2, 2, 1). dz dt=

A: If,  x2+y2+z2= 9 dx/dt = 3, and dy/dt = 5,  find  dz/dt when  (x, y, z) = (2, 2, 1). dz/dt=?

Q: sin(2t + ) dt JT 2 e2t-3 -3 4 e3 7 7 64e3 7 8. 5 4 4

A: Proceed as shown

Q: sin(2t + ) dt e21-3 4 7 4 4 64e 7

A:

Q: (2y cosx + sin* x)dx sin x dy, when x = y = =,y= 1

A: Given - 2ycosx + sin3xdx = sinx dy , when x = π2, y = 1 To find - Solve the following differential…

Q: 1. sinx siny dx + cosx cosy dy = 0 %3D 2. [2xy cos(x2) – 2xy + 1]dx + [sin(x²) – x²]dy = 0 3. y?dx +…

A:

Q: -y cos xy - 4x) dx + (- x cos xy + 2y) dy o 1. = 0 2x+3y Zar+3y 2.

A: Proceed as shown below...

Q: d?y 4- dt2 dy dy (-2) 9. + 28 + 49y = 0; ; y(-2) = 2 ; = dt dt 2 d?t dt + 9 dx dt (0) t(0) = 3; dx…

A:

Q: XZ 3) cos(x)-x²y + e + yz = 4, P (0,1,2)

A:

Q: 3. (sın 2y - 2x cos 2y) dx +( 2x cos 2y + 2xsın 2y)dy=Dd X = 2, Y = TT when

A:

Q: d*y 4)5t- dt + 3t () – (sin t)y = 0 dt 4 5)(sin x)y² + 2 y = 3x³ – 5 %3D 6) xy ? + 3 xy - 2 x³ y = 7

A:

Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

A:

Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

Q: cos v f(x, у, 2) 3D xz2 af af 2 cos y Cosv siny df = - = - = - dx x2z2' dy dz xz3 XZ af cos v %3D af…

A: Topic:- partial derivatives

Q: 5. y" – 2y' + y = 2sinx cosx y'(0) = 0,y(0) = 0 %3D | -

A:

Q: 1. d²y dy +6- dt² dt +8y=-4 cos(3t)

A: We need to solve D.E. As per Bartleby's guidelines we can solve one question from multiple question.…

Q: 2. (sin y)[x+sin y]dx+2x cos ydy = 0 sin y 3 Ans. x = C sin +3x y

A:

Q: 1 transforms the equation x dy + y = xy2sin(x) into The change of dependent variable y = dx dv A.…

A:

Q: (8 cos x cos y + 4 sin x sin 2y + 1) dx – 8(sin x sin y + cos x cos 2 2y) dy = 0

A:

Q: 1-fd dydx R = {0,1} * {2,5} y2 2-S y2 (1–5x)2 dxdy R = {0,1} * {0,2}

A:

Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

A:

Q: If f(x.v)= e-2x° cos(5x +y),- af dy O a. e-2[4xcos(5x +y) + sin(5x + y)] O b. -e-2x[4xycos(5x + y) +…

A:

Q: 1. (sin y — y sin x)dx + (сos x + х сos y — у)dy 3 0 %3D 2. (1— 2x2 — 2х) у' %3 4x3 + 4ху 3. (Зx cos…

A:

Q: Hei! If y cos(xy) dydx = x=0 y=0

A:

Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

A:

Q: *= 1+?-,y = -x²,x > 0 2. = x³(y – x)² +2, y1 = x,x > o у 1. %D = x³ (y – x)2 + dx , Υ1 - x, x > 0 dy…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.