By about how much will ƒ(x, y, z) = ex cos yz change as the point P(x, y, z) moves from the origin a distance of ds = 0.1 unit in the direction of 2i + 2j - 2k?

Q: 4. Evaluate 2.x cos y dx – x sin y dy along the elliptical path + y? = 1 from (2,0) to (0, 1)…

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Q: Consider the function 3..2 f(x, y) = cos(rxy) – a°y?. = cos(Txy) – x°y°. a) Find the equation of the…

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Q: (1) Evaluate the line integral 4xy dx + (2x² – 3xy)dy if the curve C consists of the line segment…

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Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

Q: Find the length of the curve 7(t) = (4 cos(3t), 4 sin(3t), 4t) for – 4 <t < 2 Give your answer to…

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Q: 7. Find the length along the parametric curve defined by v(t) = (t, In(cos(t))) from t = 0 andt=.…

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Q: 7. The point of contact for a tangent to the curve f (x) = º is (2,4). It intersects the x and y…

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Q: 4. Find the acute angle between the curves y = sin r and y = cos r (0 < r <) at their point of…

A: We find the point of intersection by setting them equal

Q: Apply the method of Implıcit Di fferentiation to find dy in eq (i) angle O=45 with and loPI-r=472…

A: Given, x2+y22=16x2y.....1x=rcosθy=rsinθr=16cos2θsinθ Now diffrentiating the given function with…

Q: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 ln cos t k,     0 ≤ t ≤ π/4

A: Consider the length of the curve is, r(t)=costi+sintj+(lncost)k Then,…

Q: Find T, N and B for the curve r (t) = (4 cos(5t), 4 sin(5t), 5t) at the point t = 0 Give your…

A: Find T→,N→ and B→ for the curve r→(t)=4 cos(5t),4sin(5t),5t at the point t=0give your answer to two…

Q: What is the equation of line tangent to y = sin z+1 at cos z the point (7, –1)? O y = nz – 1 O y =z-…

A: The equation of the curve is given by y = sinx+1cosx The point on the curve is x0, y0 = π, -1 To…

Q: The curves r¡(t) = (2t, t², t³) and r2(t) = (sin(t), sin(3t), 2t) intersect at the origin. Find…

A: If there are two curves y=f1(x) and y=f2(x) which intersect each other at point (x0, y0).  The angle…

Q: 5. Find the length of the curve given by x = cos t +t sin t, y = sin t – t cost, -T <t <

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Q: the detined b is Constant. Curiature a(t) =| 1 Cost, 1 sint, o of the curve d:laa)tR? where Find

A: We are given : α(t)=1rcos t,1rsin t,0 ⇒α'(t)=-1rsin t,1rcos t,0 Now, the Unit tangent Vector is :…

Q: Find the length of the curve x = cos t, y= sin t, 0 <IST. 4/2 4 IT 2/2 IT 2 2

A: Given that: x=cos2t, y=sin2t, 0≤t≤π

Q: The slope of the tangent to the curve r = 3 sin 40 at 0 = 0 is %3D Şelect one: O a. -1 3D1 O b. 0 C.…

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Q: The value of cosh(3z+1)dz, where C is the line segment from z=1 C to z= 2i. O a. (-sinh(6i+1)+sinh…

A: We have to find the value of integral,  I = ∮Ccosh(3z+1)dz  ;  where C is the line segment from z=1…

Q: . Evaluate ſſ,G(r)dA where G(r, y, 2) = arctan(y/x) and S is given by z = x² + y², with z< 9, r 2 0,…

A: According to the given information, it is required to evaluate the integral.

Q: What is the equation of line tangent to sin r+1 y = at the point (T, -1)? cos E O y= TX –1 - O y = 1…

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Q: Find the length of the curve 7 (t) = (3 cos(4t), 3 sin(4t), 4t) for –5 <t< 8 Give your answer to two…

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Q: (x,() + x(x, t) = sin(t) u(n, 0) = cos(7), at %3D %3D nER.

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Q: Which one of the following equations describes the tangent plane to the curve, f(x, y) = x² + y² +…

A: Explanation of the answer is as follows

Q: 2. Find the length of the curve 1<t<4. given by r= e'(sin t+cos t), y = e'(cos t-sin t), OS

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Q: 4. Given YZ tangent to oJ at point Y and m<WYZ = 104, %3D what is the measure of WXY?

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Q: Find the lengths of the curves x = 8 cos t + 8t sin t, y = 8 sin t - 8t cos t, 0 … t … pi/2

A: The length of the curve of any given function by the formula L=∫t1t2dxdt2+dxdt2dt. Here t1 and t2…

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

A: Given equation, V=13πr2h                          ...(1)

Q: Find the area between the two curves.

A: The area between the curves y=sec2x and y=sin2x on interval 0, π4:The area between curves is the…

Q: Find the length of the curve cos(t) + In(tan(;t)), y= sin(t), n/4 <t < 3T/4. x = %3D Length = %3D

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Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

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Q: The length of the curve defined parametrically by: x = e'cost, y = eʻsint,0 <t <, is equal to:…

A: given parametric curve x=etcost     y=etsint

Q: V. The tangent line at the point (t, y) = (- to 4'2 1 Then, the curve y = cos t is y = bt - - - a a…

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Q: Find T, N and B for the curve 7(t) (2 cos(2t), 2 sin(2t), 5t) at the point t = 0 Give your answers…

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Q: Write the tangent ratios for ZY and ZZ. 34 3 5 Not drawn to scale - unz - 5. tan Z 3 3 tan Z = 34…

A: Given:The figure,

Q: 13. Find the point on the curve 7(t) = (2 sin t, 2 cos t, t), 0<ts 7, where the tangent line is…

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Q: The lateral surface area S of a right circularcone is related to the base radius r and height h by…

A: Since, the lateral surface area S of a right circular cone is related to the base radius 'r' and…

Q: Find the point on the curve z = 5 sin(t), y = cos(t), - sts. closest to the point (2,0) . (Hint:…

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Q: The distance between two moving objects whose positions are given by ( x₁, y₁ ) and ( x₂, y₂ ) is…

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Q: - Find the aera under the curve y = cosx Form x = 0 to x = -fx sec² (ax² )dx a#0

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Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

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Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Given : x = cos2ty = cos t0 ≤ t ≤ 4π

Q: Sketch the regions enclosed by the given curves y-4 cos(7x), y- 4 sin(14x), x -D, x-/14 0.05 0.10…

A: The solution of above question is written below.

Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: It is given that,xey+sinxy+y-ln2=0.We have to find the value of dydx at the point 0,ln2.

Q: 7. Find the length of the curve f(1) = In(sin r), 0 < r < a/6.

A: Topic = Application of integration

Q: The integral that represents the length of the curve 7(t) = (t, cos (2t312), sin (2t312)), where Ost…

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Q: Find the equation of the line that is normal to the curve x cos(xy² – y) = (x + y)² at the point…

A: here option c is true

Q: a The integral that represents the length of the curve 7 (t) = <2/t,cos (2t3/2), sin (2t3/2)) where…

A: Given curve is, r→(t)=&lt;2t, cos(2t32), sin(2t32)&gt;, t∈[0,1] Now,…

Q: A curve in space is given by C = { (r, y, z) = cos(nt) ', In(10 – t²), ² + 4 for t € (0, v10) Give…

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

A: If r is the radius and h is the height of right circular cone, then find the following parts.a).…