The devil's curve (Gabriel Cramer, 1750) Find the slopes of the devil's curve y - 4y? = x* - 9x² at the four indicated points. y y4 – 4y? = x* – 9x? (-3, 2) 2 (3, 2) -3 3 (-3, -2) (3, -2) -2

Q: 2/3 Example 2: Find the length of the curve y= from x-0 to x=2.

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Q: Find the equation of the tangent plane to the graph of f(x, y) = In (14x² – 11y) at the point (1,…

A: Let us considre a two variable function z=f(x,y)  Then the equation of tangent plane  at (a,b) is…

Q: The graph of y = f(x) passes through the point (9,4). Also, the line tangent to the graph at any…

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Q: . Find the equation of the tangent line to the curve y=(x-1)^ 5 (x+4)^2  at the point (2,36). The…

A: As our company guidelines we are supposed to do only first question please repost other question as…

Q: 5-x Find the family of the curve whose slope at any point is y-3 passes through the point (2.1) and…

A: Topic:- calculus

Q: 20. The asymptotes of the curve (x – 5)² (x + 5)(x – 3) y = are A x = 3, x = -5, y = 5 в х3-3, х 3…

A: Given, y=x-52x+5x-3 Vertical asymptotes The line x=L is a vertical asymptote of the given (curve)…

Q: Find the equation of the tangent plane to the graph of 7y f(x, y) = at the point (4, –1). (Use…

A: We will find the first order partial derivatives and use the formula to find the tangent plane to…

Q: (a) Find the slope m of the tangent to the curve y = 9 + 4x2 − 2x3 at the point where x = a. m =…

A: Slope = dydx=m   ⇒ m=8x-6x2at x=a ⇒ m=8a-6a2

Q: (5) The point p = -4 is a fixed point of the function g(x) = Vx + 20. Show if it is attractive or…

A: Given that, the function is gx=x+20 and the point is p=-4. Note that, x0 is attractive if f'x0<1…

Q: The point  P(9, −2)  lies on the curve  y = 2/(8 − x). (a) If Q is the point  (x, 2/(8 − x)),  use…

A: The point on the curve y = 28-x is Px1, y1 = 9, -2 Another point Q on the curve is Qx2, y2 = 8.9,…

Q: 5. The eight curve Find the slopes of the curve y - y -x at the two points shown here. y= y -

A: Find the slopes of the curve y4=y2-x2 at the two points shown here  Find the derivative of given…

Q: 3; the slope of the secant line through the points (2, 7) and (0, 1) on the graph of f (x)

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

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Q: 3. Find the equation of a curve for which y" = 6x - 4 and which passes through (1,2) and (-2 ,5). 4.…

A: 3.y''=6x-4 and which passes through (1,2) and(-2,5).4.f''(x)=12x2+6x-4 and f(0)=4 and f(1)=1.

Q: An equation of the tangent line to a curve at the point (3, 5) is y = x + 2. if at any point (x, y)…

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Q: 2.) f(x) = x* – 2x² + 3

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Q: Find equations of the tangent lines to the curve y = (6 In(x)) at the points (1, 0) and at the point…

A: Solve by using equation of tangent

Q: 5) Find all points (x, y) on the graph of y = - with tangent lines perpendicular to the (x - 4) line…

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Q: 5.) y = x²(x – 5)²

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Q: Let f(-6) = -5 and f'(-6) = 7. Then the equation of the tangent line to the graph of y= f(x) at r =…

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

Q: The equation of a curve is y = x + 2cos x. Find the x co-ordinates of the stationary points of the…

A: The given equation of the curve is  y = x + 2cos x

Q: a) Find the point on the graph of y = e -X where the tangent line has slope - 3. b) Plot the graph…

A: Given that, y = e-x Slope of tangent line = -3

Q: 1. Use calculus techniques to sketch the curve y Vr-1

A: Given: y=x2-13 To find:  Graph of the function using calculus techniques. Concept: To sketch the…

Q: You are designing an RPG (role-playing game) for a gaming console and have decided to use an open…

A: Given that the function dx,y=e-x2y is to be minimised and maximised on the unit disc x2+y2≤900. We…

Q: 8.1 PLEASE TYPEWRITTEN FOR UPVOTE. SHOW YOUR COMPLETE SOLUTION.

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

Q: Find an equation of the curve that at each point (x, y) on the curve the normal is 3x – 1 and the…

A: Given: Normal to the curve is 3x-1    ……1 Curve passes through the point -1, 1   To find: Equation…

Q: 2 The point P(4, -2) lies on the curve y = 3 - x find the slope of the secant line PQ (correct to…

A: We will find the slope

Q: equation 2y-xedy- 942x Find the particular SoluHon of the differen tical grven mat y=3,22

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Q: Find the equation of the tangent line to the graph of the given equation at the indicated point. +…

A: Given:- (x/y) +2x-4 = (-3/4) y  To find:- Equation of tangent line at point (1, 2)

Q: 2. If you will draw the graph of y = x(x+2)², how will you sketch it with respect to the x-axis? A.…

A: Solution..

Q: 3 The point P(3, -3) lies on the curve y = 2 - x 3 (a) If Q is the point (x, find the slope of the…

A: Recall: Slope of the secant line of two given points  x1,y1 and x2,y2 is given by  y2-y1x2-x1 .

Q: The curve y = f(x) has a y – intercept of 3. The tangent to this curve at the point (x, y) has an x…

A: Given that the curve y=f(x) has a y-intercept of 3.  That means y(0)=3. also given that the tangent…

Q: Find the linearizations of sec x at x = -π/4. Graph the curves and linearizations together

A: Given function is secx and we have to find linearization at x=-π4. Linearization of a function is…

Q: 2-x )Use the guidelines of this section to sketch the curve y3x-12VX.

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Find the points on the curve y=2x3+3x2-12x+1 the tangent is horizontal.  0 (Hint: tangent is…

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Q: The values of x of the curve y =-- 4x where y' = y"

A: ddxx36-4x=x22-4d2dx2x36-4x=xAs y' = y"x22-4=x  :x2-2x-8=0x1, 2=--2±-22-4· 1·-82· 1The solutions to…

Q: (a) Find the slope of the curve y=x2-3x-2 at the point P(2, - 4) by finding the limiting value of…

A: This question can be solved using the concept of limit and equation of line in point slope form

Q: x-4 Use the guidelines for sketching the curve f (x) = In %3D x2-3x-4/

A: Consider the given function y=lnx2-4x2-3x-4 The x-intercept occur where y = 0. lnx2-4x2-3x-4=0 It is…

Q: ential equation of the family of curves y B are arbitrary constants

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Q: 2. The slope of the tangent to a curve at any point (x, y) on the curve is. Find the equation of the…

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Q: Wallis is seated on the line tangent to y=4-3x-x2 at the point (2, -6).

A: wallis is seated on the line  tangent to curve   y=4-3x-x2   at point 2,-6

Q: 2. Find the slope of the curve y 3x +1 at the point (-0). Draw the graph of the curve. KIVERSIT TLOU

A: Solution:Giveny2=3x+1  at -13,0To find Slope of the curve and Draw a graph of the…

Q: The y-intercept is (0, 0). The x-intercepts are (0, 0), (2, 0). Degree is 3. End behavior: as x →…

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Q: 5-x 8. Find the family of the curve whose slope at any point is y-3 passes through the point (2, 1)…

A: Given that slop of curve is (5-x)/(y-3) We know slope is dy/dx . Some formulas  (i). Integration of…

Q: (a) Find the slope m of the tangent to the curve y = 5 + 4x2 - 2x³ at the point where x = a. m = (b)…

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Q: b) domain {x e R, x 2 4}, range {y e R} c) domain {x e R}, range {y e R, y -2}

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Q: Find an equation of the tangent line to the graph of the function at the given point. y =V 2x3 + 8…

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Q: Let f(-3) = -7 and f'(-3) = -2. Then the equation of the tangent line to the graph of y = f(x) at x…

A: To find the equation of the tangent line

Q: The curve y=ax² +bx+c_passes through the point (1,2). The line y=2x+1 is tangent to the curve when…

A: We have to solve

Q: 3 The point P(9, -3) lies on the curve y 8 - x 3 (a) If Q is the point (x, find the slope of the…

A: the m slope of the secant line passes through point A(x1,y1) and B (x2,y2) is given as m=y2-y1x2-x1…