Find the points on the curve y = tan x, -pai/2 <x <pai/2, where the normal line is parallel to the line y = -x/2. Sketch the curve and normal lines together, labeling each with its equation.

Q: Find the point at which the tangent line to the curve r= (1+sin e) is parallel to the Х-аxis?

A:

Q: At the given point, find the equation of the tangent line, as requested. y^5+x^3=y^2+10x, tangent…

A:

Q: B) Find all the points on the curve y=tan x, -n/2<x</2, where the tangent line is parallel to the…

A:

Q: Find (a) the equation of the secant line through the points where x has the given values, and (b)…

A: Given: f(x)=2x-1 x=5 and x=10. (a) Determine the value of f(x)=2x-1 at x=5. f(x)=25-1=24=4…

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=1 and y=0 in the given equation So the point satisfies the equation

Q: find the equation of the tangent line and normal line to the ff. curves at the indicated point.

A:

Q: Find the length of the curve y2 = x3 from the origin to the point where the tangent makes an angle…

A:

Q: Find the equation of the tangent line to y = x + tan (x) where x = TI.

A: We have to find the equation of tangent line .

Q: Find (a) the equation of the secant line through the points where x has the given values, and (b)…

A: Given f(x)=3x2-5x+7, x=2, x=4

Q: find an equation for the tangent line and the normal line to the curve y = x sqrt x^2+1 for the…

A:

Q: Find the equation of the tangent and normal line to the following curves at an indicated points:

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Find equations of the tangent line and normal line to the curve at the given point. (1, 0.25) y=…

A:

Q: Find the exact length of the curve. y = Vx - x2 + sin

A:

Q: Find all points on the curve y = tan x, -p&gt;2 6 x 6 p&gt;2, wherethe tangent line is parallel to…

A: Given, y=tanx, -π2&lt;x&lt;π2

Q: On the same axes, plot the curve y = 1x, the line y = x/8, and the tangent line to y = 1x that is…

A: Given curve is y=x. Let x,y be any point on the curve. Differentiate function with respect to x.…

Q: [10] At what point on the curve y = e*is the tangent line parallel to the line y = 2x? Give answer…

A: Given curve y=ex   and line y=2x

Q: Find an equation of the tangent Iine to the ollowing curve at the point (0, 5). xe' + ye* = 5

A:

Q: Find the lines that are tangent and normal to the curve y = tan x at the point (, 1)

A:

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=1 and y=π/2 in the given function  Since both sides are equal so (1, π/2) is on the curve…

Q: Find the coordinates of the points on the curve y= x' + 5x + 3 at which the tangent: makes an angle…

A:

Q: The function f(x, y) = sin(/3x2 + 3y² ) corresponds to plot [ Select ] level curve [ Select] >

A:

Q: graph the curves over the given intervals, togetherwith their tangent lines at the given values of…

A:

Q: Find the equation of the tangent line to x? – y + y? = 21 at the point (1,5).

A:

Q: Determine the equation of the slope of the line tangent to y = tan(x) using the 4-step rule.

A:

Q: Find the points on the curve where the tangent line is horizontal and vertical. r = 1 − sin θ

A: In the question it is asked to find the points of tangent line (horizontal and vertical) to the…

Q: At the given point, find the slope of the curve or the line that is tangent to the curve, as…

A: Use derivative

Q: Find the equation of the line tangent to y = x sin(x) at the point where x = π.

A: Given:y = x sin(x) at the point where x = π.At x = π, y = π sin(π) = 0

Q: Find the equation of the tangent and normal line at the point indicated. Sketch the curve. y = x –…

A:

Q: Find the equations of the tangent and normal line to the following curve at an indicated points

A: Given that: y=31+x

Q: At the given point, find the line that is normal to the curve at the given point. 5x y-n cos y = 6n,…

A:

Q: Find a point on the curve y=√x, where the tangent makes an angle of 45 degrees with the positive…

A:

Q: Find all values of x where the tangent lines to y = x and y = x° are parallel.

A:

Q: Find the point at which the tangent line to the curve r= (1+sin e) is parallel to the х-аxis?

A: Solution: We know that, the slope of the x-axis is 0, therefore any line parallel to x-axis must…

Q: Find the equations of the tangent lines x = 2 sin 2t, y = 3 sin t at the point where the curve…

A: Consider the given equation as x=2sin2t, y=3sint

Q: What is the slope of a line normal to the curve y=tan(x)/(1+tan(x)) at x=pi/4?

A: Given the equation of the curve y=tanx1+tanx To find the slope of the normal line to the given curve…

Q: Find the equation of the tangent and normal lines to the curve y=sqrt(x) at the point (1,1).

A:

Q: graph the curves over the given intervals, togetherwith their tangent lines at the given values of…

A: Given Data The equation is y=1+cosx. The interval is -3π/2≤x≤2π. The value of x is x=-π/3, 3π/2.…

Q: Find the point of tangency and write the equation of the tangent line at this point. B

A: The tangent to a circle is defined as a straight line that touches the circle at a single point. The…

Q: Find the points on the curve r = 1– sin 0 - where the tangent line is horizontal or vertical.

A: To find out the points on the given curve, where the tangent line is horizontal or vertical.

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A:

Q: Find the equation of the tangent line and the normal line at the point corresponding to the given…

A:

Q: Find the equation of the tangent line at =n/6. r tan O

A: We Have to find

Q: Find the equation of the tangent and normal line using the stipulated conditions   2.) x2 + 2y2 =…

A: The equation of tangent line is x2+2y2=9⇒x29+y292=1we have a=3 and b=92Since, we know that the…

Q: Find an equation for the line that goes through the point (0,0) so that the tangent of the angle it…

A: Given, (x1,y1)= (0,0) tangent of the angle it makes with the x-axis=0

Q: Find all values of x where tangent lines to y=x^5 and y=x^6 are parallel.

A:

Q: Find the equation of the tangent line to the graph of y= tan x at the point where x = pi/4

A: Given Data The equation is y=tan x. The point is x=π/4.   The expression for the slope of the…

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A:

Q: image attached

A: Use chain rule:

Q: The f '(x) of the given curve is equal to -4 y = sin 3x ||

A: