Assume A = A₁ + A₂ and A, B = 0. If A₂ = kB, show that k = ● (5) (6) Use the formula x = r' (t) xr"(t) || || r' (t) ||³ 4 ✓17 function r(t)=(4 cost, t, 4 sin t) is K- - A.B ||B||2 to show that the curvature of the vector

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A:

Q: Use the formula (x) K(X) = = y = 3x4 = |f"(x)| [1 + (F'(x))²] ³ 3/2 to find the curvature.

A: y=3x4

Q: Find the extreme values of the function z= &r+2ry-3r+y+1 and show that only one of the two extrema…

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

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

A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

Q: Find the curvature of y = sin (1x) at x = 4.

A: we are given a one-variable function and we need to find out the curvature at the given point.For a…

Q: Find the curvature of the given curve y(x) = In(secx) a. 1/(Sec?x + 1) b. Cosx//1+ Cos²x C. Secx d.…

A:

Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: Use the formula x(x) x(x) = y = 2x4 * 1 + (f'(x))²]3/2 to find the curvature.

A:

Q: 2) Choose your favorite curve and apply the formula x'(t)y"(t) – y' (t)æ" (t) K(t) = (V(a(t))? +…

A: Consider

Q: For the curve defined by 7(t) = (e-t, v2 - t, e*) find the unit tangent vector and unit normal…

A: A detailed solution is given below.

Q: The curvature of a function y = f(x) is given by the expression y" (1 + (y')²)³/2 Determine a…

A:

Q: Find the curvature of ƒ(x) = ln cos x, < x < 2 -- 2°

A:

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A:

Q: Use the formula x(x) = = K(x) = y = 3x4 |f"(x)| [1 + (²²(x))²] ¹ to find the curvature.

A: Given information:Function: To find:The curvature of the function .Concept used:The curvature of a…

Q: For a function y = f(x), show that the curvature is given by к(x) = Hint: Parameterize the function…

A:

Q: ||r'(t) × r"(t)|| ||r'(t)||* 3. Use the formula k(t) to find the curvature of the space curve at t =…

A: To find The curvature of the space curve

Q: a(0)=(r(0)cos0,r(0)sin@) Find the curvature of the curve. What are the coefficients a and b if its…

A: (a) Curvature of the curve αθ=rθcosθ, rθsinθ: Let α1θ=rθcosθα2θ=rθsinθ Then, the curve αθ is given…

Q: . Find the curvature of r(!) (1², In(1), In(1)) at the point (1,0,0).

A:

Q: For the curve r-y +2xy-y+1=0: a) Find the derivative dy/dx. b) Where do the horizontal tangent lines…

A: follow the next step

Q: 8. [*] for position vector (t-1, 3-2t, 4t-t') find [*] the unit tangent [**] the unit normal, the…

A:

Q: Write a formula for the curvature K(t) in terms of ( r' (t) and r" 0) )? And prove it?

A: The curvature Kt is given by Kt=r't×r''tr't3 Now prove this formula in the following.

Q: The curvature of the curve 7 (t)={2t, 2t+1, sin2t) at t= is 4 O 1 O 1 O 2 1/818 1/2

A: Here the given curve is r(t)⇀ ==(2t,2t+1,sin2t) Here we have to find the curvature of the curve at…

Q: Consider the curve given by r(t) = where t varies over the real numbers. Find the curvature of r(t)…

A:

Q: Consider the curve r(t) = (e' sin(2t), e' cos(2t), 2e*). (a) (b) (c) Find the osculating plane of…

A: Solution: The curve is r→t=etsin2t,etcos2t,2et