Ir th line x=4+2t, ーも paralled to the plone 3x +ry +2=7-

Q: biven that y=sin(3lncx)) is a solulion of x y" + xy' +9y=0, solue x y"+ xy' +qy=0 ; y()= 2 =y'().

A: Solve Cauchy Euler differential equation

Q: xp %3D 0. dy %3D 18 + 9t2 dt xp for y = Find ||

A:

Q: at Solve thie équation use Eulers methoc- ds -t X-ツ dx x+y y(6)%=1

A:

Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: 2x Ex FIND THE DERIVATI VES %3D

A:

Q: ds-(s + et)dt=0 (find DE,prove if exact or not)

A: dsdt=s+et  It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…

Q: dy when x = - 1 and dt Given y = 6x +7x, find dx %3D = 5. dt %3D

A:

Q: 5. f'(x) dx = Choose... 6. cosh t dt = Choose...

A:

Q: Show for Re(z) > 1 dx = r(2) ((2). et - 1

A:

Q: dy/dx= tan^2 (x) / sec^2 (y), y=pie/4 when x=0

A: given,                 dydx=tan2xsec2y and           y   = π4 when x =0

Q: (b) u = Vt² + 2vt3 - 1 tan I (d) y = sec I VE-1 (f) y = VI+1

A: Since you have asked multiple subpart, as per our guidelines we are supposed to answer only first 3…

Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dæ = 0.4 Find the differential dy when…

A:

Q: sec 2x da 4. I+3 tanzx

A: Integration methods help to find the answer to the problem. Substitution of the function helps to…

Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

A:

Q: Evaluate the integrals in Exercises

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

Q: Solve dy / dx = 1 /( x^2 – 1) , for y(0) = 0. Find its maximal interval of existence %3D

A:

Q: (a) i. Find Re{sec (x + iy)}.

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

Q: dx using miscellaneous substitution will yield to secx + 1 nsforming - S 1+2 / dz √²-22² dz 1+z²…

A:

Q: af Find of f (x, y) = sin %3D dx 1+ Y COS 1+y () Option 1 sin 1+ y 1+ y Ontion 4

A: Partial derivative of a function in several variables with respect to one variable is calculated by…

Q: Gixen dw wt 3y x dt dy +2X +3 x Find the gencral oludtii, usri eign.

A: Write the given system into matrix equation as follows.

Q: valuate S S Se(3 – 4x)dV, whe e xy-plane defined by 0 < x s

A: To find: ∫∫∫E(3-4x) dV

Q: d sec (z) = dz %3D sec(z) tan(z) O sec?(z) O (2) tan(z) O tan2(2)

A:

Q: Assume that x= x(t) and y = y(t). Let y =x° +3 and xp -=5 when x= 2. dt dy Find - when x= 2. dy…

A: We have to find derivative

Q: rsin z O Find V2 +t+t2) dt.

A:

Q: dt2 d²y e. ++ 4y = 8t – 10, y(0) = 1, y'(0) = 7 %3D %3D %3D

A: As you post multiple questions According to the guideline I only solve the first problem. Please…

Q: y = sinx from x = = to x = n and the x axis 2

A: The required solution is:

Q: Line WY bisects Line UV at Y. If UY = 2x + 1 and YV = x +7, find UV.

A: Meaning of biscsts is dividing into 2 parts .

Q: Verify the integration formulas in Exercise

A:

Q: find fsub(x), fsub(y), and fsub(z): f(x,y,z)=e^yz+sinx)

A: Given,          fx,y,z=eyz+sinx

Q: fze [sin(3x)]-m(x, y, z), where m(x, y, z) = Part C. yz-1 %3D

A:

Q: Integrate h (x. y.2) = yzi+xj+xzk over the indicated path: the line segment from (0. 0. 0) to (1. 1,…

A:

Q: Fx to find Fy 15 dy dy Assuming 8x3 - 2y2 - 6xy = 0 defines y as a differentiable function of x, use…

A:

Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: JS xy dA R: rectangle with vertices (0, 0), (0, 3), (5, 3), (5,0) 166xx 16 xy dx dy = xy dy dx =

A: The solution is given as

Q: The linear approximation to f(x, y) = /2y + cos2(x) at the point (0,0) takes the form Ax + By + C.…

A:

Q: Y" - Y = { 2, %3D Ost Y(0) = Y'(0) = 0, %3D %3D t21

A:

Q: (2^)u sec (VTt) 2V7t (a) y= tan dy: dt 5- v2 (b) y = 5 + v2 dy = -5- 2iv 5 -V-5-2iv5 %3D Need Help?…

A: Both the parts are given below.

Q: what is the Folution when i =0 and t= o ? di + Ri = Esin 2t %3D dt

A:

Q: Integrate f(x,y) =x+y over the curve C: x² + y = 49 in the first quadrant from (7,0) to (0,7).

A:

Q: Q3|A: Find ý if 1-y = cot vx +2 2- y = tan v+ Vtan x 3- y = tan x+ * cot v

A:

Q: Use the Chain Rule to find dz/dt.z = sqt(8+x^2+y^2,    x = 4 ln t,    y = cos t dz/dt=

A: Please refer to the image below

Q: d tan(2) = %3D dz sec(x) O cot(x) O sec-(z) O sec (z) tan (z) O

A: We use the standard results of derivatives.

Q: (b) Evaluate (3, 10) J(0, 1) Cto (3x + y) dx +(2y - x) dy along- @ curve y= x? +1; (ü) the line…

A: Given function is 3x+ydx+2y-xdy i) Given curve is y=x2+1 Hence the integrand becomes…

Q: Evaluate f. 2xcos[y] dx- x² sin[y] dy along the parabola y = (x - 1)2 from (1,0) to (0,1)

A:

Q: Find y' and y". y = Vx In y' y" %3D II

A: we have ,  y=xlnx y'=?y''=?

Q: (a) Show that y = x* is concave upwards at the origin and y= e* is everywhere concave upwards.

A:

Q: Integrate h (x, y. 2) = yzi+xj+xzk over the indicated path: (a) the line segment from (0, 0. 0) to…

A: definite integrate calculus

Q: The longest interval in which the I.V.P y" + (tanx)y-xy x, y(1) = 3, y'(1) = 0 surlay has a solution…

A: Given,  y''+tanx y'-xy=x It is of the form,  y''+p(x) y'+q(x) y=g(x)

Q: Find fr and fy- f(x, y) = ets dt %3D f (x, y) = %3D fy(r, y) =

A:

Q: Find eauation of ny Perbola at o Ne tne foci Fz the and crankshafto f Fi Fz ny Perbola= Fi F

A: