(a) Find the slope of the tangent line to the curve y = x - x3 at the point (1, 0)(i) using Definition 2 (ii) using Equation 3(b) Find an equation of the tangent line in part (a).(c) Graph the curve and the tangent line in successively smaller viewing rectangles centered at (1, 0) until the  curve and the line appear to coincide.

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Q: 1. Find an equation of the tangent line to the curve  x^2 + y +y^2 = 13 at the point (-1, 3). ?

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A: Given: f(x)=y=5lnxx Equation of tangent to a function f(x) at (m,n) is given by y-n=f'(m)x-m

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A: The curve is y=x2+1 at the point (-2,5).

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Q: a) Find an equation for the tangent line to the curve y= 2/x at the point (2, 1) on this curve.

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Q: Find the equation of the tangent line to the graph of x2y2+ 2xy = 24 at the point (-3, 2).

A: givenx2y2+ 2xy = 24      and point (-3,2)diffentiate this equation for calculating slope of tangent…

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A: Derivative y with respect to x and then substitute the given point to find the slope.

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Q: Find an equation of the tangent line to the curve at the given point. y = (1 + 4x)8,  (0, 1)

A: The equation of the tangent at a point (a,b)on the curve y=f(x) is given by, y-b=f'(a) (x-a)

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Q: 7. Find the equation of the tangent line to the curve y = - 1-3x at x =-1 using calculus and…

A: Given curve is y=21-3x At x=-1, y=21-3·-1=21+3=24=12 So, the point is -1,12

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A: Using first principles, determine the equation of the tangent line at point (2,2)on the curve f ( x…

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Q: (15) Find an equation of the tangent line to the curve, xy3 − y = x2 + 5, at the point (1,2).

A: Find the slope

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A: Given function as y=sec2x

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Q: 8. Find the equation of the horizontal tangent line to the curve y = -x + yx.

A: For horizontal  tangent line put the derivative  of function equals to zero

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Q: Find the equation of the tangent to the curve y = x/2x² + 7 at x = 3.

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Q: 6. Determine the equation of the line tangent to y = x+ tan r at the point (7, 7).

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A: Find the slope at x = -pi.

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Q: 5. Find the equation of the tangent line (slope-intercept form) to the 5 at the point (6,1). x-1…

A: To determine the equation of the tangent line.

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Q: roblem 5. Find the equation for the line tangent to the curve y√ = 3x√√y - 10 at x =

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