3. Lapluce of lunction fct)_is givan by -Fes)-S Pct) d. 6-F4) - C) et dt C. -00 SA

Q: Ez fand Pi) Pow = * in Tesm of Po, Pg

A: For a function fx, it is known that  fx=∑kAkPkx                        (i) Where Pk is the Legendre…

Q: 7. 2 SECANTS WHOLE WHOLE = WIOLE • OUT SIDE SECANT AND 6. TANGENT IMIDE PIECE • PIECE = PIECE •…

A:

Q: What is a parametrization of a curve in the xy-plane? Does a function y = ƒ(x) always have a…

A: Parameterization of a curve: Parameterization of a curve in xy plane is a process of rewriting the…

Q: Find an appropriate parametrization for the given piecewise-smooth curve in R'. The triangle formed…

A: Given that the triangle formed by travelling from the point (1,2,3) to (0,-2,7), to (6,4,2) and back…

Q: Evaluate ze dV, where E is the portion of the ball centered at the origin of radius 5, x + y+< 25…

A: Given Where E is portion of the ball centered at origin, radius 5 and lies in first octant. In…

Q: Exercise 8. Show that the sum of the angles of a geodesic triangle on a surface of positive…

A: We will use the Gauss–Bonnet theorem to prove the given statement.

Q: Find the favily of orthogonal trageclores %3D

A:

Q: 4. Does there exist a simple closed unit-speed plane curve with curvature less than or equal to 2…

A: In a simple closed unit-speed plane curve, curvature =1r According to the question, Area of the…

Q: Describe the interual(s) on which the funchion is continous. %3D XA

A:

Q: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: Which lines or line segments or rays must be drawn or con- structed in a triangle to locate its a)…

A: (a) The orthocentre is the point where all the three altitudes of the triangle cut or intersect each…

Q: 55. A point moves along the intersection of the elliptic parab- oloid z = x+ 3y and the plane y = 1.…

A:

Q: Is the below statement True or False? The parametrization for a given curve is unique.

A: No. Parametrization of a curve is not unique. For example y = x2 can be written as (t,t2) or…

Q: Use Green's theorem to evaluate $(xy + 3x²)dx + (3y – 2x)dy, along C, where Cis the triangle with…

A: Given Integral ∮(xy+3x2)dx +(3y-2x)dy along c where c is the triangle with vertices (0, 0), (0, 3)…

Q: .Calculate the dstance between tve point (3, -2) and the plane Z Xty-2+1=0.

A: The distance between the point (a, b, c) and the plane Ax+By+Cz+D=0 is given by,

Q: Compute paramenc curve Ogiven by bu Iine of the X= eEsinct) 二e ato t=

A: To Determine: Compute the tangent line of the parametric curve given by  Given: We have   x=etsint…

Q: )2. Find the paramehic from the cuve check whether the cure is a repulor cuve. Alo reparzmetije the…

A: We have to find the parametric form of the curve

Q: The centroid of an obtuse triangle is outside the triangle. true or false?

A: solution ======== The centroid is the concurrent point of the three medians in a triangle. It is the…

Q: 7. Which surface is parameterized by ř(u, v) = (u, uv, v) for –1 < u <1 and –1< v< 1?

A: r→(u, v) = u, uv, v for -1≤u≤1 and -1≤v≤1The parametric curve is  Option C is correct.

Q: Exercise 7. Show that the curvature of a circle of radius r is , and the curvature of the line is…

A: Show that the curvature of a circle of radius r is 1r and the curvature of the line is zero.

Q: Give a geometrical interpretation of torsion.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Exercise 5. Show that there exists at most one closed geodesic on a cylinder with negative…

A: We will assume S ⊂ R be a surface homeomorphic to a cylinder and with Gaussian curvature K &lt; 0.…

Q: What is a parametrization of a curve in the xy-plane?

A: we have to tell what is parametrization of a curve in the xy-plane?

Q: Find a parametrization for the line segment joining points (0, 2) and (4, 0) using the angle 0 in…

A: Modify the given figure as shown in Figure 1.

Q: Find the isogonal trojecdories of x*+y² =r² at 45",

A:

Q: 4) Find the families of lines of curvature of the surface z = r + y? .

A: Given: z=x2+y2

Q: Use Stoker Cur theorem to evaluate. IF - ds S Where F= of radius I with x ] +ya³k ands is the +yx³k…

A: Given That  ∬Curl F →·dS→ F→=yi-xj+yx3k To Find: evaluate  ∬Curl F →·dS→  using strokes theorem

Q: Let S be the surface parametrized by R (u, v) =< u, uv, uv

A: It is given that, the parametrized surface is R(u,v)=u, uv, uv2, 0≤u≤2, 0≤v≤3.  We have to calculate…

Q: The sphere x² + y² +z² = 100 has the center (0,0,0) and a radius of length 50. Select one: True…

A:

Q: Must two rays with a common endpoint be coplanar? Must three rays with a common endpoint be…

A: We know that two rays with a common endpoint must be coplanar and three rays with a common endpoint…

Q: Find the orthogonal trojectories of y(sx +c) = 1.

A: Given query is to find the orthogonal trajectories to y (3x+c) = 1.

Q: 3. Infer some rosults from the axioms and illustrations of the three- line and four- line…

A: As per your requirement, answer of 3rd part is mentioned below

Q: Must the centroid of an isosceles triangle lie on the altitude to the base?

A: The centroid of an isosceles triangle lie on the altitude.

Q: consider surface s with parami Glusv) = cu vo uv) Compute Pa, 7 Nas Tu, Tv o of s olso compute the…

A: Given surface is, G(u,v)=(u,v,uv)

Q: Find The or rthoganal tajeclolies. ! d faly Curver r= 4C cose, where C be being parameer

A:

Q: 3. Find the orthogonal trayectories to the cuve y = ax²- acx Is held fixed. 3 .2 %3D where a

A: The curves that cut every member of a given family of curves at right angles, is called an…

Q: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

Q: 3. Please give clear explanations

A: The parametrization of a surface S is given by       G(u, v)=(u, v, uv) where D is u2+v2≤1.

Q: Exercise 3. Show that the Gaussian curvature of a surface which is home- omorphic to the torus must…

A:

Q: Sketch the reglon enclosed by the given curves. Dedde whether to iIntegrate with respect to or y.…

A:

Q: Sketch the triangle with vertices O,P = (4,0, 2) and Q = (4, 3,0) and compute its area products.…

A: To find the area of triangle

Q: 4) Find the families of lines of curvature of the surface :=r+y

A: The answer is given in handwritten format --

Q: What is the general process to fit random 3D points to a surface?

A: Hint: Here 3D points are given we need to plot them on a surface. Write the general process to plot…

Q: Every plane curve has a unique parameterization. O False. OTrue.

A:

Q: Write down the condition of tidal resonance in terms of a (mean ocean width), lambda, and n; where n…

A: The tidal resonance occurs when the tide excites one of the resonant modes of the ocean. The effect…

Q: Determine whether each of the following statements is true or false, and explain why Simpson’s rule…

A: Given statement is  Simpson’s rule usually gives a better approximation than the trapezoidal rule.

Q: What is a parametrization of a curve in the xy-plane? Does a function y = ƒ(x) always have a…

A: Parametrization of a curve in the xy-plane:Parametrization of a curve consists of both equation and…

Q: Give arc-lengtu porametriz atian of the line which an Hhe tangent planes of and (1,2,9). is Hhe…

A:

Q: Determine the area bounded by the conic sections y = x² – 6² and y = 6² – 2². O 576 O 183 O 281 O…

A:

Q: Find a parametrization for the line segment joining points (0, 2) and (4, 0) using the angle 0 in…

A: Given: The line segment joining (0, 2) and (4, 0). Do the construction as in below figure