(a). Find the slope, m, of the tangent to the curve y=2 sqrt x at the point where x = a.

Q: Find an equation of the tangent line to the graph at the given point. 3(x? + y?}² = 100(x² - y?),…

A: 3x2+y22=100x2-y2 3x4+2x2y2+y4=100x2-y2 3x4+6x2y2+3y4=100x2-100y2 3x4+6x2y2+3y4-100x2+100y2=0 to find…

Q: Find ​(a) the slope of the curve at the given point​ P, and ​(b) an equation of the tangent line at…

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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 an equation in the form y = ax? + bx + c whose graph has an x-intercept at x = -1 and a tangent…

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Q: Find the slope of the tangent to the curve. (If an answer is undefined, enter UNDEFINED.) x2 + 2xy…

A: Given, x²+2xy+5= 0 Differentiating w.r.t x we have, dx²/dx + d(2xy)/dx +d(5)/dx= 0 2x+ 2y.dx/dx +…

Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

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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 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: 2.1 Identify and sketch the graph of y = /9 – 4x². Show all the necessary points on the curve and…

A: We can square the left-hand side and right-hand side then we get y2 = 9-4x2

Q: Determine the equation, in y= mx + b form, of the line that is perpendicular to the slope of the…

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Q: Find the equation of the tangent line and normal line to the curve ? = √? − 3 and whose normal line…

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Q: Find the constant k so that the line with equation y = kx is tangent to the circle with equation (x…

A: Given:The line y = kx is tangent to the circle (x - 3)^2 + (y - 5)^2 = 4.

Q: Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the…

A: Given

Q: (a) If F(x) = 12x/(3 + x2), find F '(3) and use it to find an equation of the tangent line to the…

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Q: Find the slope of the tangent to x^2+y^2=14^2 at x1=6 in the first quadrant. This is the equation of…

A: First find that point in first quadrant where we have to find the slope of the tangent than take the…

Q: Given the equation of curves: y = x2 + 7x + 6 and x - 2y = 6. Find the slopes of the tangents of the…

A: We begin by finding the points(s) of intersection of the 2 curves y =x2+7x+6  &  x-2y = 6y…

Q: c) Finally, draw a large and clear sketch of the graph of f(x) = 2² – 2 and illustrate the tangent…

A: The point slope form y-f(x0)=f'(x0)(x-x0) is the standard equation for tangent line, where (x0,y0)…

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

A: We will find the tangent equations.

Q: Find the equation of the tangents to the graph y = x^3 + 3x^2 - 15x -20 at Ox-y-9=0 O9x-y-48 = 0 O9y…

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Q: Find the slope of the line tangent tangent to the graph a the given poin 4 y = ,x = 6 5+x 4 m = 121…

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Q: Find the point(s) on the graph of the following equation that have horizontal or vertical tangent…

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Q: h(x) = -3x° – 5x + 20r + 60r

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Q: Given the curve y= x^3 - 4x +1 . Find the equation of the tangent at the points where the slope of…

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Q: Consider the following curve y = 2x^2-9x+1 a. Find the slope m of the tangent line at the…

A: Given         y=2x2-9x+1→           1       slope of the tangent line is        dydx=ddx2x2-9x+1…

Q: The graph of y=a3x2+a2​, where a is a constant is called the witch of Agnesi.   a. Let a=6 and find…

A: a). Given, y=216x2+36 Differentiating with respect to x, we get…

Q: Find an equation for the tangent to the curve at the given point. y = x2 - 4, (2,0) О А. у32х- 8 В.…

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

A: topic - equation of a tangent line

Q: Consider the following curve. y = V1 - 24x Find the slope m of the tangent line at the point (-1,…

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Q: Consider the following curve. y = 2x2 - 10x + 1 Find the slope m of the tangent line at the point…

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Q: (a) Find the slope, m, of the tangent to the curve y = 9 + 5x2 - 2x3 at the point where x = a. m =…

A: Slope of the tangent is derivate of the given equation at that point.

Q: Find an equation of the tangent line to the graph at the given point. x?y² - 9x² – 4y² = 0, (4, 2/3)…

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Q: 4. 4. () = a北

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Q: Sketch a graph of y? = x* – 12x , find the coordinates of the points on the graph of y? = x³ – 12x…

A: giveny2=x3-12xwhen tangent line is Horizontal ,then slope will be zero.differentiate the…

Q: Find equations for the tangents to the circle (x - 2)2 + ( y - 1)2 = 5 at the points where the…

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Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

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

A: GIVEN y2=3x+1 at(-1/3,0) we need to find the slope of the curve and graph the curve

Q: (a) If G(x) = 4x2 -x3, find  G'(a) and use it to find equationsof the tangent lines to the curve…

A: Gx=4x2-x3 Now differentiating with respect to x, we get G'x=42x-3x2=8x-3x2 Now slope of the tangent…

Q: (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve…

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Q: (a) Find the slope, m, of the tangent to the curve y = 2 + 5x? – 2x3 at the point where x = a. m =…

A: On finding slope of the given curve we will differentiate 1st then using formula to find equation of…

Q: 13. Show that there are no tangents to the curve y = can be concluded about the graph? 2x+1 4x +3…

A: We have to prove that negative slope is not possible for graph.

Q: Find the slope of the tangent to x^2+y^2=19^2 at x1=7 in the first quadrant. This is the equation of…

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Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: Equation of tangent to a curve y=f(x) at a point (x0,y0) is y-y0=f'(x0)(x-x0)

Q: The equation of a curve is given by f(x) = (6x² − 7) (2x + 6). What is the slope of the tangent line…

A: The slope of tangent line on a curve f(x) that touches the curve at x = c is m = f'(c).

Q: Find ​(a) the slope of the curve at the given point​ P, and ​(b) an equation of the tangent line at…

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Q: Find an equation for the tangent to the curve at the given point. y = x3/2 , (5, 62.5)

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

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Q: find an equation for the tangent line to the curve atthe given point. Then sketch the curve and…

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