Answered: 69) 21) The tangent line of y = In(x² -…

Math

Calculus

69) 21) The tangent line of y = In(x² - 8x + 9) is horizontal at x = A) – 2 B) 2 C) 4 D) – 4

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

See similar textbooks

Related questions

Q: Evaluate the line integral ſc 2y dx + 6x dy where C is the straight line path from (4, 1) to (6, 5).…

A: Given query is to find the integral.

Q: Evaluate the line integral S 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). So…

Q: 5. Prove that whole length of the curve x3 + y2/3 = a/3 is 6a.

A: Given that x23+y23=a23 To find the length of the curve:…

Q: Find the equation of the tangent plane to th surface 3x? + 5y? + 4z2 = 24 at the point (1, –1,2). 1.…

Q: Evaluate (x+ y)ds where C is the straight-line segment x = t, y= (4- t), z=0 from (0,4,0) to…

A: Given that x=t,y=4-t,z=0 from (0,4,0) to (4,0,0) evaluate ∫cx+yds

Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

Q: 2. Prove that the following curves are intersecting with a right angle: 5y-2x+ y –x*y =0 2y+5x+x*…

A: Given curves are 5y-2x+y2-x2y=0and2y+5x+x4-x3y2=0

Q: Compute Sc(2x + V) ds, where C is the curve from (0,0) to (2, 4) along y

A: Given

Q: Find the point(s) on x = 3 - y that are closest to point A = (1,0).

A: Given: Curve x=3-y2 and a point A(1,0).

Q: 13. Show that the length of the portion of any tangent line to the ball x2/3 + y2/3 cut off by the…

A: Given: The equation of the ball is: x23+y23=a23...........(1) We have to show that the length of the…

Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

Q: If C is the line segment which begins at (-2, 1) and ends at (2, 4), evaluate the line integral: e+y…

A: Given, The line integral ∫Cex+yds Where C is line segment from the point -2,1 to the point 2,4 So,…

Q: Evaluate F- dr where F(, y, z) = (1.5yz cos(ryz), 1.5xzcos(ryz), 1.5xy cos(ryz)) and C (*) is the…

A: We need to evaluate the line integral between the two points.

Q: 8how that the square of the leng point on the curve by = (x + a)° , length of the subnormal at that

A: Subnormal and Sub tangent: Allow y=f(x) to be the differentiable curve at point P. Let the tangent…

Q: Compute f, f for f(z) = sin(5z) and path y that is the line segment from 3 – 6i to -6+ 6i.

Q: I. Determine la ecuación del plano tangente a la superficie dada en el punto especificado 1. z = 4x2…

Q: If C is the line segment which begins at (-2, 1) and ends at (2, 4), evaluate the line integral: et…

Q: Evaluate the line integral 2ydx + 5xdy where C is the straight line path from (1, 2) to (6, 5). Г…

Q: Compute x²z ds where Cis the line segment from (0,6,–1) to (4,1,5).

Q: 7 Prove : id Is perpendicular line to ra duic at its outer end point ,then t ang ent to the cirde is

Q: Determine una ecuación del plano tangente a la superficie dada en el punto especificado *:(-4, 2,…

Q: Suppose that the plane tangent to z = f(x,y) at (-2,3,4) has equation 4x + 2y + z = 2. Estimate…

A: As the given plane tangent to z=f(x,y) at (-2,3,4) is 4x+2y+z=2, that is z=2-4x-2y thus the…

Q: 2. Approximate f,(3,5) using the contour diagram of S(x, y) in Figure 14.9.

A: Given query is to find the value of fx(3,5).

Q: ompute the line integral ∫C [2x3y2 dx + x4y dy] where C is the path that travels first from (1, 0)…

A: The line integral is given ∫C2x3y2dx+x4y dy Consider fx,y=x4y22. ddxx4y22=12·4x3y2+22x4y…

Q: Compute (ax + by² + cz) dS over the sphere x +y +z² = 1.

Q: Evaluate the line integral Sc (2x² − 3y) dx + xy dy, where the curve/path C is the line 3 y = 2/2 x…

Q: 9. Evaluate the line integral / (2x – 3y) ds; where C is the line segment from (-1,0) to (0, 1)…

A: 9.

Q: Let C be the line segment from point (0, 1, 1) to point (2, 2, 3). Evaluate line integral yds. C

A: To evaluate the line integral

Q: The base of a three-dimensional figure is bound by the line x = y² and the y-axis on the interval…

Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral 2|(xdx…

Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

Q: Let y = [3] and u = [2] to the line through u and the origin. Compute the distance from y

Q: The area bounded by the curve y = 4r and the lines z = 2 and I=8 above the I- aris is O 240.00…

Q: 4) Suppose that the level curves of a function z = f (x, y) consists of straight lines. Must the…

A: Given that level curve of a function z=f(x,y) consists of straight lines.

Q: 4. Evaluate where C is a circle of radius 2, parallel to the r - z plane and around the y-axis with…

A: Using the parametric equation of the curve C.

Q: Let C be the curve of intersection of length of C from the origin to the poi

Q: If C is the line segment from (1, 4, 2) to (3, 2, 1), evaluate the line integral y+ 2) ds.

A: Express the line segment in its parametric form and then use the formula below to evaluate the line…

Q: Evaluate the line integralf, (xy + z)ds along the line segment C from (1,2,3) to (-1,1,5).

Q: (is)Find the eguakion af the line tangent to y=ro* át (!,10')

Q: Does the the paraboloid z = 1 – 2x² - - y² have a tangent plane at some – x + y + z = 1?

A: Introduction: Let P0=(x0,y0) is a point in the domain of f, and S is a surface defined by a…

Q: Evaluate the line integral 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). Sc…

Q: Evaluate the line integral ∫Cx2yds along the segment of the line y=x from the origin up to the point…

Q: In the standard (x,y) plane, what is the distance between (3, 4) and (6, 2)?

Q: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

Q: Obtain the dirfferential equation of the family of plain curves given 1. All circles passing…

Q: 17. The tangent of the acute angle between the lines y = 4x – 3 and y = x – 2,is D

Q: Find the exact length of the curve. y = In(1 - x²), o sxs

A: Find dy/dx, then put it in the arc length formula.

Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

69) 21) The tangent line of y = In(x² – 8x + 9) is horizontal at x =
A) – 2
B) 2
C) 4
D) – 4

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Cartesian Coordinates$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

If x and y are elements of an ordered integral domain D, prove the following inequalities. a. x22xy+y20 b. x2+y2xy c. x2+y2xy
aIf HP=4, PJ=5, and PM=2, find LP. _ bIf HP=x+1, PJ=x1, LP=8, and PM=3, find x. _
Set up the line integral ∫c x2z ds, where c is the line segment from (1, 6, -1) to (- 4, 1, 5). (No computation)
1) Evaluate the line integral ∫_c (2x − y) dx − (x+ 3y) dy , where C is a straight line from (1,1) to (3,5), followed by a horizontal line from (3,5) to (5,5).
if z=xarctan(y/z), find ∂z/∂x at x=0, y=1, z=1
If F = (5xy --- 6x(2^) i + (2y - 4x) j, evaluate along the curve C in the xy plane, y = x(^3) from the point (1,1) to (2,8).
Show that the minimum distance from the origin to a point on theplane ax + by + cz = d is
Evaluate the line integral ∫Cx2yds along the segment of the line y=x from the origin up to the point (2,2) (see Figure 3).
Compute the line integral∫C [2x3y2 dx + x4y dy]where C is the path that travels first from (1, 0) to (0, 1) along the partof the circle x2 + y2 = 1 that lies in the first quadrant and then from(0, 1) to (−1, 0) along the line segment that connects the two points.
Evaluate∮C (x + 3y)dx + ydy where C is the Jordan curve given by thegraphs of y = e^x, y = e^−x and the horizontal line y = e^−1a) By Green’s theoremb) By direct computation
If UV bisects XY at point W, which statement must be true?
Show that the path given by r(t) = (cos t,cos(2t), sint) intersects the xy-plane infinitely many times, but the underlying space curve intersects the xy-plane only twice.