10. Given two points P1(0,2,-1) and P2(2,0,-1), find the perpendicular distance from the point P3(3, 3, -1) to the line P1P2.

Q: Evaluate the integral of the following using Miscellaneous Substitution dx 4. Sa

A: We can evaluate the given integral by using the substitution u = x⅙  and the following formulas.

Q: Find the arc length of the parametric curve. = 4 cos(t), y = 4 sin(t), z = 3t; 0<t<T %3D

A: Use arc length formula

Q: TE: Round your answer to two decimal places when neec r(t) = cos(nt)i – In(t)j+ vt – 12k - omain is:…

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Q: Find the formula for the nth term of the arithmetic sequence.  Use the formula to find the 20th term…

A:

Q: Find the arc length L of the graph of r(t). r(1) = t³ i+ t j+V6r? k, 2 <t< 5 k, 2 <t < 5 L = i

A: Given : r(t) = t3 i + t j + √6 t2/2 k 2 ≤ t ≤ 5 Now, r'(t) = 3t2 i + j + √6 t k Arc Length :

Q: Determine whether the vector field F(x, y, z) = x'5 i + y'5 j + z!5 k is free of sources and sinks.…

A:

Q: 10. At what point on the parabola y = 3 x 2 + 2xisthetangentlineparallel totheline y = 10x -2? Use…

A: Given query is to find the point where tangent line to the parabola is parallel to the given line.

Q: Determine whether the series converges using the limit comparison test. Σ20k²+k-20 k=1 The series

A: We have to determine whether the series converges or not

Q: How many times will you use double angle identities to solve the integral of (sinx)^2*(cosx)^2dx?…

A: ∫ sin2x cos2xdx

Q: Exercise (2) - Solve using paper solution. d²y dy 2- - y + x = 0 dx² dx Solve using…

A: Find your answer below

Q: me origin is 6i + 8j, then the me direction of a = 3i + 4j at

A:

Q: X 75 ft 0 A pole stands 75 feet tall. An angle is formed when wires of various lengths of a feet are…

A:

Q: 2. Evaluate the indefinite integrals. (a) fx² - 2e*dx (b) Evaluate (3-4x)¹5 dx

A: We have to evaluate the indefinite integral

Q: eorem to evaluate the integral. Assume that the curve Cis oriented coun dy, where Cis the triangle…

A:

Q: Which of these statements is False? А. (а?)3 — а6 Вв. а?а — а = a' a2 C. a3 = a-1 D. a? + a³ = a°

A:

Q: What is the difference between a function and a parametric curve? Make sure to justify your answer.…

A: This is a problem related to function and parametric equation for the same. Based on the general…

Q: )4 Evaluate (nx) dx

A:

Q: Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check…

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Q: Find a power series solution around xo = 0 for y" – xy = 0

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Q: x + 21 x + 1] 4 2. Find x and B, if B is symmetric. %3D

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Verify the formula F.n dS div FdV in the Divergence Theorem by evaluating the surface integral and…

A:

Q: (x) is an even function, and if f 6 f(x) dx = 15, find f³, f(x) dx.

A: Given query is to find the value of the Indicated integral.

Q: Solve for the Taylor series of the given function about the point x = 1. You can write the first 5…

A:

Q: H.W: Use the comparison test to determine the following series converge or diverge: 1 3" +5 n=1

A:

Q: dx 4 XVx - 4

A: We need to find the solution for the given  integral by trigonometric substitution.

Q: Determine a, and as for each arithmetic sequence. See Examples 3 and 4. 29,. 24. -3, -7, -11,... 25.…

A: Since, the student has mentioned to solve only question number 24, so we are solving accordingly…

Q: Evaluate the definite integral by interpreting it in terms of areas. 8 (4x - 24)dx stion

A:

Q: 10. Using the graph below of the function f(x), identify the approximate interval(s) where the first…

A: Given that,

Q: Suppose that f(x, y) is differentiable at the point (3, 1) with f(3, 1) = 4, fx (3, 1) = 2, and fy…

A:

Q: Using any method, find the value of F. dr if F(1, у) — (бе" + ye")i + (e* + 5xe") j and at C :r(t) =…

A:

Q: Q5. Which of these statements is False А. (а?)3 — а6 в. а?а? — а 5 2.3 a a2 С. a3 = a¬1 D. a + a' =…

A:

Q: Ex: Show that if v, u, w are any vectors, then (H.W.) ux (v x w) + v x (w x u) +w x (u x v) = 0.

A: Dot Product Property :- a.b = b.a = a*b*cosθ

Q: Write the logarithmic equation in exponential form. log7343 = 3 7³ = 77 7343 = 2 7³ = 14 3437 = 2 7³…

A: We will write in exponential form.

Q: Sorry im running out of questions

A:

Q: Find the area between the innér and outer loops of the limaçon r = 2 – 4 sin .

A: This is a problem related to area of the polar curve. based on the graph of limacon curve we will…

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A: To find the equation of family of curves whose slope is given .

Q: Use the Divergence Theorem to find the flux of F(x, y, 2) = (a* – e)i+ (y³ + sin z)j + (2³ – cy)k 3…

A:

Q: Use the One-to-One Property to solve the equation for x. 5x+1=25 x = 5 x = 1 x = 2 x = 4 x=3

A: given that  5x+1=25 Or 5x+1=52  On comparing  X+1=2  So x=1

Q: H.W: which series converge and which diverge: 1. E 1 1 2. n=1 n=1

A: This is a problem related to series and sum calculation. Based on the general formula and concepts…

Q: Find the surface area of the region that comes from rotating the given curve about the y-axis: x =…

A: If x=x(t) and y=y(t) then surface area of the region rotating about y-axis is given by…

Q: 4+ 2t + et dt

A:

Q: Verify Green's Theorem by evaluating both integrals v² dx + x² dy = / / dA ax for the given path. C:…

A:

Q: ||r'(t) × x r" (t)|| Use the formula k(t) to find k(t). r(t) = t’i + tl5j %3D K(t) :

A: The given formula is; κt=r't×r''tr't3 And rt=t2i+t15j   As we know that; The Power law; ddxxn=nxn-1

Q: 7. Find the partial fraction decompositions of the following rational expressions. a) b) (x²+11x) dx…

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Q: Integrating factr: (y -x + xy cotx)dx + xdy= 0(*). Determination of integrating factor for egn of…

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Q: Write the logarithmic equation in exponential form. log7 2 49

A:

Q: Perform

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Q: Verify Green's Theorem by evaluating both integrals aN v? dx + x² dy | dA ду ax for the given path.…

A: Given problem:-

Q: Verify the formula F-n dS : div F dV in the Divergence Theorem by evaluating the surface integral…

A:

Q: full

A: We will find the polar equation.