8. The surface of a water wave is described by y 5(1+cosx), for -nSxST, where y = 0 corresponds %3D to a trough of the wave. Find the average height of the wave above the trough on [-t, T].

Q: 4. Evaluate: S. yx?dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t2 , (0 st< 1).

A:

Q: Find the slope of the tangent line at a for the graph of the f(x) = xtan z y(x) be given implicitly…

A: a) Here we have to find the slope of the function f(x)=xtanx .......................... (1)  Let…

Q: Find y': e siny + el cost esinz-esiny O a. e cosy te cosT O b. eysinz-e sinzy ос e sinzte siny…

A: Given problem:- ex sin(y) +ey cos(x) =10  find:- y'

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

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Q: Find the external in the isoperimetric problem of the extremum of subject to f(y² +xy'- :“)dx= 2,y…

A: Consider the functional  Iyx=∫x1x2Fx,y,y'dxwith the conditions yx1=y1 , yx2=y2and Iyx=∫x1x2Gx,y,y'dx…

Q: Q1/ Evaluate So (x² + 3y²) dy dx using Simpson's 1/3 rule in x-axis and Simpson's 3/8 rule in y axis

A: 1 Given integral is ∫03∫01x2+3y2dydx. We have to evaluate the given integral  by using Simpson's 13…

Q: Use Euler's method to find the approximate value of y correct up to 4 dy =x-y² decimal places for…

A: The numerical solution of the differential equation is the value of the function that satisfies the…

Q: 2. Find the equation of the tangent plane and the normal line at the point (0 ,1 , 2) on the surface…

A:

Q: Use Euler's method with h = 1/4 to compute approximate values of y(1) for t.y'= y(sint), y(0)=2.

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Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

Q: 2. Use Euler's method to find the approximate value of y correct up to 4 dy decimal places for…

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

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Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: Given Volume of cone isV=13πr2hwhere r is radius and h is height and h is constant .

Q: 4. Evaluate: S. yx²dx + xzydy + xz?dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

A:

Q: W3:- Estimate y(0.2),using Euler methe ere y': = -y?cosx „y(0)=1

A: Here we have to estimate y(0.2), using the Euler method with step size h=0.1 where,

Q: 2. Find the equation of the tangent plane to f(x,y) = sin(x² +y) when x = 0, y = T. 3 and r - cost

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Q: Find the length of the curve y = ln(sec(x)), where 0 is less than or equal to x which is less than…

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Q: How would I evaluate ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above the cone Φ =…

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Q: The equation of the tangent to the curve y=4+ sin' x at X=0 is O y = 4 O y = 2 O y = 6 O y = 3

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: dw by using Chain Rule. (Your answer should not include z ond y. dt = z+v? z = cost + sin t and y=…

A:

Q: 1 The volume of a right circular cone of radius a and height y is given by V = ²y. 3 when x = 6 and…

A:

Q: (4) Evaluate sin(yz)dr+xz cos(yz)dy+ry cos(yz)dz, where C is any curve joining the point (0, 0,0) to…

A:

Q: Suppose L is the tangent line of f (x) = csc T at x = 2 . Where does L intersect the y-axis? Note:…

A: We have to find

Q: How can I evaluate ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above the cone Φ =…

A:

Q: olve the following initial value problem using variation of parameters: y" + 4y = cos 3x y(0) = 0,…

A:

Q: The linear approximation at z = 0 to sin(4z) is A+ Bz where A is: and where B is:

A: Linear approximation is found by L(x)=f(x)+f'(x)(x-a) Differentiate L(x) with respect to x.…

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: find the general salution of ly-3y12)de = xdy,

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Q: where t is a non-zero parameter. Show that dx 28 Given that x=z and y==. 1+r Hence find its value at…

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Q: 1.Evaluate S. (x² + y² + x²)-²ds where C is the helix x = cost, y = sint, z = 1 for 0 < t ST

A: The length dS is: ds=dtdxdt2+dydt2+dzdt2=dt-sint2+cost2+02=dt

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: The linear approximation at a = O to sin(7x) is A + Bx where A is: and where B is:

A:

Q: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

Q: what is of point Fyl-2,0) fexsy)=(x3ーy+g)s

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Q: 30. Find an equation for the tangent plane to z = f(x, y) at (3, -2) if the differential at (3, -2)…

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Q: H.W: Use the chain rule to find the derivative of w= x + y with %3D dw respect to t dt with x =…

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Q: Use Euler's Method to approximate y(10.8) with step sizeh 0.2. dy = 3y + x- 5 y(10)= 0 %3D dx

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Q: Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z =t², (0 <t< 1).

A: As per the question we are given a line integral, which we have to evaluate around the curve C.

Q: Find the first three approximations using Euler’s method for theinitial value problem            y'…

A: Given   y' = 1 + y,         y(0) = 1, starting at x0 = 0  with dx = 0.1.

Q: 3) Consider the fonction (a) The tangent plare to the graph of fCx,y) at the point Co,0) is (b) At…

A:

Q: Use Taylor's formula at the origin to get a cubic approximation of the function: f(x,y) = ln(2x + y…

A: Given function f(x,y)=ln(2x+y+1) and a,b=0,0 Taylor's expansion  at origina,b=0,0 to get a cubic…

Q: 4. An earth satellite moves in a path that can be described by x2 72.5 = 1 71.5 where x and y are in…

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Q: Find an equation of the tangent llne to the về at the given poln 6x y = (x + 1)2' (0, 0)

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

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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: Admit that for all (x, y), af (х, у) — х dx se (x, y) = 4y ду calculate g' (1) = f(2 cost, sint).

A: We have to prove 4y*f'x - x*f'y = 0 Also calculate g'(t).

Q: 1 The volume of a right circular cone of radius x and height y is given by V TXʻY. Suppose that the…

A: Given that:                        Volume of the cone, V=13πx2yV=204π cm3x=6y=17

Q: th 2 Evaluate khe fulawingcartesian integrat by changing theminte equiv alent Pelarintegrals: E 4-y…

A:

Q: The volume V of a right circular cylinder of radius r and height h is V=πr2h (a) How is dV/dt…

A: