Math

CalculusQ&A LibraryFind parametric equations for the lines in Exercises 1–4. 1. The line through the origin parallel to the vector 2j + k 2. The line through the point (3, -2, 1) parallel to the line x = 1 + 2t, y = 2 - t, z = 3t 3. The line through (1, 1, 1) parallel to the z-axis 4. The line through (2, 4, 5) perpendicular to the plane 3x + 7y - 5z = 21Start your trial now! First week only $4.99!*arrow_forward*

Question

Find parametric equations for the lines in Exercises 1–4.

1. The line through the origin parallel to the vector 2j + k

2. The line through the point (3, -2, 1) parallel to the line x = 1 + 2t, y = 2 - t, z = 3t

3. The line through (1, 1, 1) parallel to the z-axis

4. The line through (2, 4, 5) perpendicular to the plane 3x + 7y - 5z = 21

Tagged in

Math

Calculus

Find answers to questions asked by students like you.

Q: What are the Ratio and Root Tests? Do they always give you the information you need to determine con...

A: A mathematical series can be convergent or divergent subject to certain conditions. Ratio test and t...

Q: consider the product of 3 functions w= f x g x h. Find an expression for the derivative of the produ...

A: Given functions are f, g , hTheir derivatives are given by f ' , g ' , h '

Q: Use f(x) = 5x − 3 and g(x) = 4 − x2to evaluate the expression. (f ∘ g)(x) (g ∘ f)(x)

A: Given,

Q: Find the lengths of the curves in Exercises 13–14. 13. y = x^1/2 - (1/3)x^3/2, 1<=x<= 4 14. x ...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: f(x) =16 − x2, g(x) = x + 2 Find (f + g)(x)

A: Given functions are

Q: Show that the Taylor series for ƒ(x) = tan-1 x diverges for |x|>1.

A: Using Taylor Series.

Q: What is an infinite sequence? What does it mean for such a se-quence to converge? To diverge? Give e...

A: Infinite sequence:

Q: Find all polar coordinates of the origin.

A: We know that when we convert cartesian coordinates into polar coordinates, then we use the relation

Q: Solve the inequality. Write your answer in interval notation. |5x - 4| ≤ 7

A: Click to see the answer

Q: Find the measures of the angles between the diago-nals of the rectangle whose vertices are A = (1, 0...

A: The given vertices of the rectangle is A = (1,0), B = (0,3), C = (3,4), and D = (4,1).Use the given ...

Q: describe the given set with a single equation or with a pair of equations. The circle in which the p...

A: sphere of radius 5 centered at the origin is given by:

Q: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the...

A: Given: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope...

Q: Find the limit analytically

A: Given, limit function is

Q: Show that the tangents to the curve y2 = 4px from any point on the line x = -p are perpendicular.

A: The given curve is,

Q: How are integral tables typically used? What do you do if a particular integral you want to evaluate...

A: In simpler terms, the table of integrals offers readymade solution to different types of integral te...

Q: what Taylor series would you choose to represent the function near the given value of x? (There may ...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: What is an autonomous system of differential equations? What is a solution to such a system? What is...

A: Click to see the answer

Q: What consequence does the lack of uniqueness of polar coordi-nates have for graphing? Give an exampl...

A: Click to see the answer

Q: Find an equation for the ellipse of eccentricity 2 /3 that has the line x = 2 as a directrix and the...

A: To determine the equation of the ellipse.

Q: Find the distance from the point (3, -4, 2) to the a. xy-plane b. yz-plane c.xz-plane.

A: a) Distance of (3, -4, 2) from xy plane:On xy plane , z=0. So, This point is 2 units away from the z...

Q: find the component form of the vector. The unit vector obtained by rotating the vector {1, 0}135° co...

A: The unit vector obtained by rotating the vector {1, 0}135° counterclockwise about the origin.

Q: Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y =...

A: Click to see the answer

Q: Marcos traveled for 2 hours and 17 minutes on Interstate 17 as he drove (without stopping) a distanc...

A: Given:Marcos travelled a distance of 155 miles in 2 hours and 17 minutes.

Q: Let a and b be constants with 0 < a < b. Does the sequence {(an + bn)}^1/n converge? If it doe...

A: Click to see the answer

Q: What is the rule when dividing rational expressions

A: Click to see the answer

Q: Solve the equation. e4x+4e2x-21=0

A: Let us suppose y = e2x, substitute the value of y in the given equation:

Q: Use the equation ƒ(x) = ƒ(a) + ƒ′(a)(x - a) + ƒ′′(c2) /2 (x - a)2 to establish the following test. L...

A: For the given function to determine its behaviour at a critical point x=a, use second derivative tes...

Q: Find derivative and evaluate the derivative at given value: f(x) = (sinx)ln5x ; a = PI/2

A: The given function is,

Q: In Exercises 1–3, a. Identify the equilibrium values. Which are stable and which are unstable? b. Co...

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,...

Q: Find the areas of the surfaces generated by revolving the curves in Exercises 31–34 about the indica...

A: We’ll answer the 31th question since we answer only one question at a time. Please submit a new ques...

Q: Which of the following are always true, and which are not always true? Give reasons for your answers...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: What is an alternating series? What theorem is available for deter-mining the convergence of such a ...

A: The alternating series test.

Q: What are the Direct Comparison Test and the Limit Comparison Test? What is the reasoning behind thes...

A: Direct comparison test:

Q: Solve the initial value problem tdy/dt + 2y = t3 , t> 0, y(2) = 1

A: Click to see the answer

Q: Find a vector of magnitude 3 in the direction opposite to the direction of v = (1/2)i - (1/2)j - (1/...

A: Given,

Q: Show that a. cosh iu = cos u, b. sinh iu = i sin u.

A: To show that

Q: I need to compute each limit. I have attached the problem as a photo.

A: Given:

Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval nota...

A: Consider the provided function,f(x) = (x+8)/(square root x)The rational function is continuous every...

Q: Find an equation for the set of points equidistant from the point (0, 0, 2) and the x-axis.

A: To determine the equation for the set of the points.

Q: Find equations for the sphere whose centers and radii are given in center(1,2,3) radius sqrt(14)

A: To determine the equation of a sphere.

Q: The parabola y2 = 8x is shifted down 2 units and right 1 unit to generate the parabola ( y + 2)2 = 8...

A: Given equation of parabola after shifting

Q: Solve the differential equation listed below:

A: Separate the variables.

Q: Find the X and Y intercepts of y= 1 - the square root of 1 -x2

A: Given,

Q: Find the binomial series for the functions in Exercises 11–13. 11. (1 + x)4 12. (1 - 2x)3 13. (1 + ...

A: As per our norms, I am going to solve only one question as you have posted multiple question so plea...

Q: Show that the curves 2x2 + 3y2 = 5 and y2 = x3 are orthogonal.

A: To show that the two curves are orthogonal.

Q: dy/dx of pi

A: pi is a constant.It has value 3.14 approx.

Q: Looking for help for all of the questions with lines next to them.

A: Since you have asked multiple questions, we will solve the first three questions for you. If you wan...

Q: Let u = 5i - j + k, v = j - 5k, w =-15i + 3j - 3k. Which vectors, if any, are (a) perpendicular? (b)...

A: To determine the vector which are,Part (a) ParallelPart (b) Perpendicular

Q: Find an equation for the parabola with focus (4, 0) and directrix x = 3. Sketch the parabola togethe...

A: Given that the focus of the parabola is (4, 0) and its directrix is x = 3. Observe that the focus li...

Q: What are Taylor polynomials? Of what use are they?

A: Let us take a function f, a specific point x = a (called the center), and a positive integer n, the ...