pumt (0 ). (b) Illustrate part (a) by graphing the curve and the tangent line on the same screen. y 10 1 3 6 (0, 5) V0, -5) -6 -8 – 10 -3 -2 -1 1 2 3 y y 10 8 -3 -2 -1 (0, 5) (0, -5) 6F -8 X

Q: A: Find the lines that are tangent and normal to the curve x + xy - y =1 at the point (2, 3).

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

Q: C. Find the slope and the equation of the tangent line to the curve. 1. у %3D х2- 4х + 1 at (2, -3)

A:

Q: Which points on the curve of x^2-xy-y^2=5 have vertical tangent lines? A. (1,-2) B. (2,-1) and…

A: I have used the fact that slope of vertical tangent line is infinity

Q: x = 2r - 61+3 y=r+21. Then the curve C has horizontal tangent line at1=-1

A: Find the horizontal tangent line

Q: X = --6t-1 2 Find all points on the graph of that have either a vertical or horizontal y=- -9t +1 3…

A: Here given x=3t22-6t-1y=t33-9t+1

Q: Find the equation of the tangent line to the curve y = (2 In(x))/x at the points (1, 0) and (e,…

A: To find the tangent line equations to the curve: y=2 ln(x)x at points (1,0) and e,e2. Note that, the…

Q: 3(x2 + y2)2 = 100(x² – y2), (4, -2) y = Lemniscate y -4 -2 /6 (4, -2) -4 -6 2. 2.

A: This is related to equation of tangent to a curve

Q: Find all points (if any) of vertical tangency for the curve represented by x = t? + 2t – 3 and y =…

A:

Q: Find the equation of the tangent line to the curve y = 5sec(x) -10cos(x) at the point (pi/3,5).…

A: Given query is to find the equation of the tangent.

Q: 3x2 + 5y2 = 8 curve is given. a) Find an equation for the tangent line at (1,-1) 24 b) Show that y"…

A:

Q: find an equation for the tangent to the curve at thegiven point. Then sketch the curve and tangent…

A: Given that, y=1x2

Q: (b) The curve y = x +3x, from x 1 to x = 3 (c) The ,2 1 from 2 to g

A:

Q: The curve y = 1/(x 2 + 1) is called the witch of Agnesi after the Italian mathematician Maria Agnesi…

A: y=1x2+1we have to find tangent line at x=±1

Q: Wite the equation of the tangent the curve live to y=X*tlex-9 at Cl, -2)

A:

Q: Sketch the curve f(x.y) = c together with Vf and the tangent line at the given point. Then write an…

A:

Q: 3. Find the equation of the curve at every point of which the tangent line has a slope of 4.x. (a) y…

A: Slope = dy/dx

Q: Consider the curve x+y² +2xy=4x . (a) Find all the x-intercepts of the curve. (b) For each of the…

A: The given curve is: x3+y2+2xy=4x...(1)

Q: The equation of the tangent line to the curve at the given point. x2 v2 2-13 = (1, 1) is %3D 100 4…

A:

Q: Find an equation for the tangent to the curve at the given point. y = x2- 3, (-4, 13) Oy = -4x- 19…

A:

Q: a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to…

A:

Q: 24. Consider the curve defined by the equation below and a point (2, 1) on the curve. What is the of…

A: Given query is to find the slope of the tangent line at point (2,1).

Q: For the curvey ax + bx- + 12x - 7. what values of a and b will make the tangents to the curve at x =…

A: We have to solve the problem

Q: Consider the following curve. x - 1 y = x + 1 Find y'(x). y'(x) = Find equations of the tangent…

A: solution: the objective is to find the equations of tangent lines

Q: a) Find the equation of the tangent plane to the graph of the curve f(x,y) = x² + y² at the point…

A: Mentioned below is the answer

Q: Two ground stations are located by its coordinates as A (0,0) and B (0,5), the unit being 1 km. An…

A:

Q: a. Determine the points where the curve 4x + 5y - y = 6 has a vertical tangent line. b. Does the…

A: a)  curve is 4x+5y2-y=6         Slope of tangent line is m=dydx    Differentiate the above equation…

Q: For the curve y = ax+ bx + 12x- 7. what values of a and b will make the tangents to the curve at x…

A: Given, The curve  y=ax3+bx2+12x-7 We have to find the value of a  and b such that tangent to the…

Q: y = 4x4+(3+51)x3+5x2-(100+1)x-400. What is the slope of the tangent on this curve at x=2.5?

A: Slope of the tangent to the curve y=fx at x=x0  Differentiate equation of curve with respect to x…

Q: Let y = 1+ eX (a) Find an equation of the tangent line to the curve y at the point (0, 3). (b)…

A:

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx %3D

A:

Q: Sketch the curve x = 3sin2t, y = 4cos2t

A: This question is taken from the function in which we have to sketch the given function parametric…

Q: (2) Find all points on the graph y = x3 - 12x + 9 with horizontal tangents. Find dy d2y and dc d2…

A: Given:

Q: C: y= 3 17 + 12 4 | +

A:

Q: (a) Find an equation of the tangent line to the curve y = 14/(1 + e-X) at the point (0, 7). (b)…

A:

Q: a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to…

A:

Q: y=x^2+5  Determine at which point, (x,y), in which the graph has a horizontal tangent line.

A:

Q: 2.x? Sketch the curve y= x² - 1

A: y=2x2x2-1 y=2x2x-1x+1

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x

A:

Q: Find the equation of the tangent line to y = at the point (1, 16). + y = Use a calculator to graph…

A: This question is based on application of Derivative.

Q: a. Determine the points where the curve 5x + 3y - y= 5 has a vertical tangent line. b. Does the…

A:

Q: (b) Show that the points of inflexion of the curve y = (x- a) (x – b) lie on the | line 3x +a =4b.

A:

Q: Find y' if x³+y³ = 6xy . Find the tangent to the folium of Descartes x³ + y³ = 6xy at the point…

A:

Q: curve that lies a. to the left of z = -1.39 b. to the right of z = 1.96 c. between z =-2.16 and z…

A: We have given that. Standard normal    X~N( μ =0 , ?= 1 )   μ =0 , ? = 1    Z-score =( x - μ )/?…

Q: 1.) Tangent to the parabola z= x2+3y2 , x = 1 at point ( 1, 2, 13)

A:

Q: a. Determine the points where the curve 4x + 2y -y =1 has a vertical tangent line. b. Does the curve…

A: Consider the given curve 4x + 2y2 – y = 1

Q: 2. Consider the graph of the equation r+ry+y- 5. Find the slope of the tangent line at the point…

A:

Q: Sketch the curve f(x,y) = c together with Vf and the tangent line at the given point. Then write an…

A:

Q: 25. Consider the curve defined by the equation below and a point (2, 1) on the curve. What is the…

A: topic - equation of a tangent line

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.