Find a point on the curve y=√x, where the tangent makes an angle of 45 degrees with the positive x−axis.

Q: Find the slope of the tangent line to the curve a? – 2xy + 2y° - 63 at the point ( – 3, – 3).

A: Given : x2 - 2xy + 2y3 = -63

Q: Find the slope of the tangent to the curve r=−6+5cosθ at the value θ=π/2

A: Given curve is

Q: Find the tangent plane to the equation 5e*- öy at the point (12, 24, 5).

A:

Q: ズ Find an equation of the tangent line to the curve y= 8 arccos at the point (1, 7). 2

A: we have to find the equation of the tangent to the curve y at (1, π)

Q: Find the slope of the tangent line to the curve - læ? 3xy – 4y 144 at the point (3, 3). Ouoction ||

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Q: Use the diagram at the right to find m24. R tangent line

A: Tangent chord angle is half of the arc angle.

Q: Find the slope of the tangent line for the curve r=3+5cosθ when θ=π/6

A: Concept - If a function f(x) is given then slope of the line tangent to it at x=a is given by -slope…

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

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Q: Find the slope of the tangent line to the curve (a lemniscate) 2 (z? + y?)° = 25(x² – y²) at the…

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Q: Find the equation of the tangent line to the curve y = IVI at the point (9, 27). %3D y = 9x(sqrt(27)

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Q: Find the slope of the tangent line to the curve - 3x + lay+ 3y = 199 | %3D | at the point (1, – 4).

A: We are given a curve and we need to find out the slope to the tangent line at the point (1,-4). For…

Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4)

A: Equation of the tangent line

Q: Find the slope of the tangent line to the curve - 2.x? + 3xy + y – 118 - at the point (3, – 4).

A:

Q: Find the slope of the tangent line to the curve - 2x2 + 3xy + 4y° 3 242 at the point (- 1, 4).

A: Given curve is -2x2+3xy+4y3=242. To find: Slope of the tangent line to the given curve at the point…

Q: Find the points on the lemniscate where the tangent is horizontal. 8(x2 + y2)2 = 81(x2 − y2)

A: The equation for the lemniscate

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

A:

Q: Find the slope of the tangent line to the curve - 4x – 3ry + 4y° = = 14 at the point (- 3, 2).

A:

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

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Q: Find the slope of the tangent line to the curve - l2? – 2æy – 2y³ = 19 at the point (3, - 2).

A:

Q: Find the coordinates of the point Pin Figure, at which the tangent line passes through (5, 0).

A: Given figure is  where suppose that the coordinate of point P is P=a,b

Q: Find the equation of the tangent line at (1,2) for x'+2y = 9 y- A= B(x - C)

A: point (1,2)  ; x3+2y2=9 In the given point x is 1, y is 2

Q: Find equation of the tangent an ine to the carve ad X= Xo, ' line

A:

Q: find the tangents as direccted to the curve y = x4 – 4x3 + 2x2 – 4x + 15, perpendicular to the line…

A: Given that  y=x^4-4x^3+2x^2+4x+15  Line is x+8y=7

Q: At what points is the tangent horizontal or vertical?

A:

Q: Find the slope of the tangent line to the curve la? + 4xy – 2y = 185 at the point (- 3, - 4).

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Q: Find the x-corrdinates at which the tangent line to y=(x-(6/8))^8 is horizontal.

A:

Q: Find the slope of the tangent line to the curve - 2? + 4xy – 4y° = 44 at the point (– 2, – 2).

A: On solving this we will get

Q: Show that the tangent line to the curve y = x3 at any point (a, a3) meets the curve again at a point…

A: Proof: The given curve is y=x3. Obtain the derivative of the function as follows: dydx=ddxx3…

Q: Show that the tangents to the curve y2 = 4px from any point on the line x = -p are perpendicular.

A: The given curve is,

Q: Find the slope of the tangent line to the curve – 2x? – 2xy 19 at the point (4, – 3). Preview

A:

Q: Question 2

A: To determine the tangent line to the curve.

Q: Find an equation of the tangent line to the curve atthe given point.y =sqrt ( 1 + x 3 ),…

A: Given, y=1+x3 , (2,3)

Q: Find the point (in the first quadrant) on the lemniscate 2(x2 + y²)² = 25(x² - y²) where the tangent…

A:

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

A: Topic:- application of derivatives

Q: Find the slope of the tangent line to the curve r = 3-2sin(θ) at the point (3,pi).

A:

Q: The slope of the tangent line to the curve C at the point (1, 2) is A) 4 B c) 2 D - 4 2.

A:

Q: The slope of the tangent line to the curve C at the point (1, 2) is (A) 4 (B -2 c) 2 D -4

A: Solving the problem by finding the slope of the tangent.

Q: Find the points on the curve where the tangent is vertical. x=1³-3t, y-t³-31²

A: First we find dy/dx

Q: Find the slope of the tangent line to the curve la? + 4xy + 2y 32 at the point (- 4, 2). -

A:

Q: Find the slope of the tangent line to the curve - la2 – 3xy + 3y° = 29 at the point (- 1, 2).

A:

Q: Find the equation of the tangent to y = 3ex + 3ex that is parallel to y = 6ex + 5.

A:

Q: Find the slope of the tangent line to the curve - 22? – 3xy – 4y = 115 at the point (1, – 3).

A: The given equation is -2x2-3xy-4y3=115 To find the slopedydx of the tangent line at a point 1, -3…

Q: Determine the equation of the tangent line to the graph of y = y2 – x² at the points (분 ) and (블, )

A:

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 the equation of the tangent and thhe to the Pollo wing cunve uhen x = 1 (2x2- Ja)2 normal .

A:

Q: Find the tangent plane to the equation 5e* бу at the point (12, 24, 5) Z =

A:

Q: Find the points on the curve y = x3 + 3x2 9x + 4 where the tangent is horizontal. smaller x-value…

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Q: image attached

A: Use chain rule:

Q: Find all values of æ where the tangent lines to y = x³ and y = x* are parallel.

A:

Q: For what value(s) of x is the line tangent to the curve y = xV6 - x horizontal? Vertical?

A: Given curve is: y=x6-x Differentiating with respect to x we get,…