Let y = 1 + e-x* (a) Find an equation of the tangent line to the curve y at the point (0, 5). (b) Illustrate part (a) by graphing the curve and the tangent line on the same screen. y y 1 3 -3 -2 -1 -4

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A: We are given that f(x) = xx and x ​= e.

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A: 2(x2+y2)2=25(x2-y2)2(x4+y4+2x2y2)=25x2-25y22x4-25x2=-25y2-2y4-4x2y22x4-25x2=-25y2+2y4+4x2y2different…

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

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A: y=In xx,  (1,0),(e,1/e) Find y'              quotient rule :fg'=f'g-fg'22…

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A: The equation of given curve is, y= x2 + ex −e The point of tangency is (1,1)

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A: the equation of the tangent ( x0, y0 ) to the curve y=f(x) is    y – y0 = f ′(x0)(x – x0)

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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 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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A: We can find the answer as below.

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

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A: To find an equation of the tangent line to the graph of y=e-8x at the point (5,e-40).

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A: Topic = Derivative

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