The linear approximation at I = 0 to sin(3r) is A + Br where A is: and where B is:

Q: Find the value of integral | (x + y + z)ds, where C is parmeterized by 7(t) (12 sin(3t), 10 cos(3t),…

A: Let’s suppose that the three-dimensional curve C is given by the parameterization, x=x(t), y=y(t),…

Q: To obtain the General Solution of si What will be the form by separation of variables? cosv A)…

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Q: Find the value of integral | (x + y + z)ds, where C is parmeterized by F(t) = (12 sin(3t), 10…

A: Given: ∫C(x+y+z)ds, where C is parametrized by r→(t)=12sin(3t), 10cos(3t), 211cos(3t) for 0≤t≤π.

Q: dy Given y = In(tan 0), find 0 such that 4, where 0< 0 <T 2

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Q: Find the differential of the given functions. a) f(x) = sin(cos(22)) CoS %3D 2x b) g(x) x3 – 7x

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Q: I am having trouble evaluating ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above…

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Q: Find the value of dy/dx at the point defined by the given value of t. x 5 sin t, y = 5 cos t, t= O…

A: Given, x =5sint  y =5cost We have to find the value of d2ydx2 at t = 3π4

Q: The linear approximation at r 0 to sin(2r) is A+ Br where A is: and where B is:

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Q: Given: tan-1(e0.13-0.8) Get the local linear approximation to estimate the value of the given

A: According to question given that tan-1e0.13-0.8

Q: Obtain the general solution using separation of variables. dz = a(cos 0 dz + z sin 0 d0) %3D

A: Separation of variables.

Q: Find the approximate value for f(r, y) = sin(a7zy + In(y)) at (0.03, 1.04). Take = 3.

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Q: Given the linear approximation at a = 0, determine the smallest value of x such that the linear…

A: the linear approximation of f(x) at a is :…

Q: Let the velocity of a particle be given by v(t) = –sin(t). What is the displacement of the particle…

A: We need to find displacement and total distance.

Q: Give estimates, using linear approximation, for v9.2 and sin ( +0.02).

A: 9.2 Now let, fx=x,  x=9  &amp;  ∆x=0.2 Differentiating with respect to x, we get f'x=12x Now,…

Q: The radius r and height h of a right circular cylinder are related to the cylinder’s volume V by the…

A: It is given that, the height (h), radius (r) and volume (V) of a cylinder are related by the…

Q: After using z = X - y as substitution, the DE (x-y)^2 * dy/dx = a^2 (a is constant) transforms to…

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Q: Q: IF the value of (t) change from sin(“,) to cos( ",5. Find the dF for dx f(x, t) = V1+t³ Sa f(x,t)…

A: To find dFdx, whereF=∫αxβxfx,tdt, and fx,t=1+t3

Q: = f (x, y) is differentiable and x=u cos v and y =u sin v. Show that z = Oz Oz 1 + ди + и

A: According to question given that z=f(x,y) is differentiable x=u cos(v), y=u sin(v)

Q: бл Approximate sin by using a linear approximation with f(x) = sin x. 13 (等) z f(a) + f ' (a)·h = c,…

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Q: The velocity of a particle moving back and forth on a line is v = ds/dt = 6 sin(2t) m/sec for all t.…

A: Given:

Q: Find dz/dr if z as a two variables function in r and y is defined implicitly by y3 + x22 + r sin r…

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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: Let y, = sin(t) be a solution to t y" -y' +4 t y=0. If y(t) is the solution to the I.V.P ty" -y' +4…

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Q: Find the approximate value for f(r, y) = sin(a7zy + In(y)) at (0.03, 1.04). Take a = 3.

A: We have to find the linear approximation of the given function around suitable point.

Q: 3. Given that the acceleration function of an object moving along a line is a(t) = 3 cos(t)-2 sin(t)…

A: Proceed as shown

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

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Q: An integrating factor for y'+8z°y = sin z is given by (a) 2z (b) In(z*) (c) z4 (d) 5e2z

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Q: For what value(s) of t will the slope of a line tangent to x = 6 sin t, y = t² + t be undefined, for…

A: Here we have to find the slope of the tangent line.

Q: The equation of the tangent line to f(r) = at z = 1 is y = ar +b and the tangent point is (1, c).

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Q: Calculate sin(x)dA where R is the triangle in the xy-plane bounded by the x- axis, the line y = x,…

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Q: Given f(x, y, z) = xe"y + sin(xyz), find fyzz

A: Derivatives of: Sin x is Cos x Cos x is -Sin x u

Q: Find dw/ dt at the given value for the following functions 1) w=x² + y²₁ x = cos(t), y = sin(t), at…

A: Sol

Q: use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1…

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Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: Given z = sin(1 - 2). x = 2 – ts and y = 2t – s - then calculate when t = -1 and s = -1. dt

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Q: Given that f(x) = sin a cos' r +2 (sin r + a)' +, the value of the constant and the least value of f…

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Q: dy Given y³ In x + x¹e³y = sin-¹(xy), compute da

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Q: Find the value of integral | (22 + y² + 2)ds, where C is parmeterized by F(t) = (cos(4t), sin(4t),…

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Q: Find the most general antiderivative of f(x)=6e^x+5 sec^2(x), where -pi/2

A: Please see the answer below

Q: Let y = sin(5r). If Ar = 0.1 at a = 0, use linear approximation to estimate Ay Ay = 0.0087 Find the…

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Q: Solve the equation F '(t) = sin t+ | F(t – u) cos u du for F(t) with the condition that F(0) = 0.

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Q: Given the implicitly defined function sin(r²y³) + y³ = r + y I dy dy and dx2 find at the point (x,…

A: Topic = Derivative

Q: The velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for all t.…

A: given the velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for…

Q: Use Taylor's formula to find a quadratic approximation of f(x,y) = 9 cos x cos y at the origin.…

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Q: Find the directional derivative of Du f(2,1) in the direction of: d = 7i + 2j To f(x, y) = In(Ges…

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

Q: use Euler's method to obtain an approximation to four decimal places of the indicated value by first…

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Q: For the smooth curve, find any points where the tangent line is either horizontal or vertical. x(t)…

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Q: 18. The equation of the tangent line to 2² sin T # 0 f(x) = 0 x = 0 at r = 0 is 1 (a) y = -x (b) y =…

A: Note:Since you have asked  multiple questions ,we will solve first question for you.To get remaining…