Q: Find the point on the curve 4x' +a'y = 4a', 4< a < & that is farthest from the point (0,-2).

Q: Make the curve y=ax*+bx³+ cx²+ dx+e pass through the points (0,3) and (-2,7) and at (1,4) have a…

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Q: 5. Show that the equation of the tangent to the curve y = Inx + kx at x = 1 always passes through…

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Q: Find the length of the curve x = 49 sec* t – 1 dt with 3 - - 6. Length is

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Q: Find the points where the tangent line to y =2+4 is horizontal (Critical points)

A: We need to find points where the tangent line to y=xx2+4 is horizontal. In other words, we need to…

Q: Find an equation of the tangent to the curve x = 5 + In t, y = t2 + 2 at the point (5, 3) by two…

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Q: Find an equation of tangent equation is 2x+6y=3. line to the graph of y=x+lax that is perpendicular…

A: We need to find the equation of the tangent line to the graph y=x+ln(x) that is perpendicular to the…

Q: Find the tangent line to y = x -x+7 at x = 7. ,2 The tangent line to y = Vx -x + 7 at x = 7 is y =

A: We have to find tangent line

Q: 2. Find the equation of the tangent line to the curve y = x² – 2x - 3 that is parallel to the line x…

A: Given: The tangent line to the curve y=x2-2x-3 is parallel to the line x+y=1. To Find: The equation…

Q: he tangent line to y = f(1) at (-3,9) passes through the point (9,-3). Compute the following.

A: The slope of the line passing through the points, (x1,y1) and (x2,y2) is given by .

Q: 36 at the point (1,12). x2 +2 Find an equation for the tangent to the curve y D O A. y= - 8 O B. y=…

A: The equation of the tangent line: - A line's point-slope formula is y – y1 = m (x – x1). To…

Q: 2 Find the equation of the tangent line to the curve y =xNx +5 at the point (2,6)

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Q: The Normal to the curve 2x² – y² = 1 at the point (1,1)

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Q: The slope of the line tangent to the graph of y = In(x²) at x = e² is %3D

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Q: Find the equation of a tangent line to the curve y= 2x3 - 3x2 - 10x +1 which is perpendicular to the…

A: The equation of the line is      x+2y-6=0⇒y=-12x+3       in the form of line equation y=mx+c  So,…

Q: 12. The line y = 8x + b is tangent to the curve y = 2x². Determine the point of tangency and the…

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Q: 2. Find the equation of the tangent line to the curve y = x2 - 2x -3 that is parallel to the line x…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find the length of the curve defined by y = 3 ln from x = 8 to x = 9.

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Q: The tangent of the curve x^2+y^2--7 * 2xy3DO at the point (1,1), is a. y-2-х. О b. y=x-2. O С.…

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Q: Find the slope of the line tangent to the curve x + sin(y-π) = 2x3 + ey at thr point (-1,0).

A: Find dy/dx

Q: ngent line to the curve y= In(x4 + 1) at x

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Q: 3) Find the equation of the tangent line to the curve 6y³ – xy² + cos (xy) = 7 - at the point (…

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Q: The slope of the tangent line to the curve y = 4/x at the point (3, 4/3) is: Must be written in y =…

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Q: Find the equation of tangent and normal lines to the curve xs sin(2y) = y cos(2x) at the ㅠ ㅠ point…

A: Solution of this question is

Q: Find the point of intersection of the tangent line to y=sin 2x) at y=0 and the line x+2y=5-

A: Given: y=sin(2x)  and y=0       substituting y=0 in y=sin(2x)then    0=sin(2x)         2x=0…

Q: 5. Find the equation of the tangent plane of sin(xyz) = x + 2 y + 3z at the point (2, -1, 0).

A: We have given the surface X,Y,Z at the point (2,-1,0). We have to find the equation of the tangent…

Q: 12. Find the x-coordinate of the point on the graph of y= Vx where the tangent line is parallel to…

A: From the given data: x=1 x=4

Q: Find the slope of the line tangent to the curve x + sin(y+π) = 2x3 + ey at the point (-1,0). Show…

A: Topic:- application of derivatives

Q: 1) Find the equation of the tangent line to the curve: x* + xy – y = 7 at (3,2) %3D

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Q: 2х at (1,1) (x+1) Find the equation of the line tangent to y = a) x-2y =-1 b) 2x-у - 1 c) х-у -2 d)…

A: First I have written the formula of tangent line to a curve at given point, just use them for given…

Q: 3. Determine the gradient of the tangent at a point (2, 5) to the XY graph with the implicit…

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Q: 24)) Since the tangent of the curve y = x ^ 5 + ax - 3 at the point x = 1 is y = x -b, then b =?

A: Given that y=x-b is the tangent of the curve y=x5+ax-3 at the point x=1.

Q: Find the equation of the tangent to y-cos 2x at the point 0. Oal y--2- Ob) y- 2x+ O) y--+1 O d)…

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Q: .2 Find the tangent line to y = x-x+2 at x=2.

A: Given - A function To find- Equation of tangent

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x = is %3D

A: We need to find slope of normal line.

Q: Find the slope of the line tangent to the x³ – 2x + 1 at x = 2 curve y %3D %3D O-10 O 1/10 O-1/10 O…

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Q: The tangent line to the curve ³ + y³ = 9xy at the point (4,2) intersects the y-axis at y = -1. -2.…

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Q: 2. Find the coordinates of the points on the curve y = r' - x² – x +1 where the tangent line is…

A: Solution:- step-by-step solution of above  question is given below.. The given curve is  y=x3-x2-x+1…

Q: Find the slope of the tangent to the curve r+ 2xy + y = 16 at (1, 3). The slope is VEnter undof if…

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Q: find the slope of the curve x = e^-tcost2t, y=e^-2tsin2t at the point t= 0

A: find out the slope of the curve at t=0

Q: 9. Find the equation of the curve whose y" e*. = - cos x + 6x + 4 with horizontal tangent at the…

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Q: What is the equation of the tangent line and normal line to the curve y = -8 at (4, – 4)? Оа. TL: 2x…

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Q: Equation of the tangent to the curve y = 1+eX/2 at x = 0 is O x+2 y =4 2x + y = 0 2y -х- 4 O x+ 2y =…

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Q: Find an equation of the tangent line to the curve at the given point. y = 4.9x – x², (3,5.7) - y =…

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Q: Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)

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Q: Find the equation of the tangent plane to the graph of f(x, y) = In (13x² 10y²) %3D at the point (1,…

A: Solution is written in below steps.

Q: Consider the curve satisfying y" = 6x and is tangent to the line y = 5– 3x at x = 1. What is y' (2)?…

A: Given: y''=6xand tangent to the line y=5-3x at x=1To find y'(2)=?

Q: Find all (x,y) points where x² +4y² +4x- 8y+4 = 0 has horizontal or vertical tangent lines.

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Q: 12)What is the slope at (1,2) for curve define by xy^2=4?

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Q: 6. Find the equation of the tangent line to the curve 2x3 + xy + y° = 4 at the point (1, 1).

A: Firstly we can find slope .i.e, dydx at (1,1). Then slope intercept form  y-y1=m(x-x1)