Find equations of the tangent lines to the curve y=(5ln(x)) / x at the points (1,0) and (e, 5/e) at the point (1,0) y=  at the point (e, 5/e) y=   Illustrate by graphing the curve and its tangent lines.

Q: Find the equation of the tangent and normal line of the function y^3 +3xy + x^4 = 5 at the point (1,…

A: y3+3xy+x4=5 Differentiating with respect to x, we get…

Q: A function f has the tangent line y=2x+1 at the point (3,7). Find the equation of tangent line of…

A: Given data:     The given expression for the function is: y=2x+1. The given point is: (x1,y1)=(7,3).…

Q: Find an equation of the tangent line to the curve at the given point. y = 9ex + x,  (0, 9)

A: Given: y=9ex+xx1=0y1=9 The objective is to find the equation of tangent line to the curve

Q: 13. Find an equation of the tangent line to the curve at the given point (use the definition of…

A: The equation of the curve is given by y = 2x2+1 The point at which the tangent line of the curve…

Q: Find the equations of the tangent lines to the graph of y = In |x| at x = 1 and x= - 1. The equation…

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Q: Find the first derivative of the given function by a. definition or increment method. b. formula…

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Q: equation of the curve at every point of which the tangent line has a slope of -e-².

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Q: Consider the equation and the given point. f(x) = (x – 3)(x² + 6), (1, –14) (a) Find an equation of…

A: (a) The equation of the curve and the point is given as,

Q: Find the equation of the tangent line to the curve at the given point. (4,3) y= square root of 2x +…

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Q: Find equations of the tangent line and normal line to the given curve at the specified point. y =…

A: Find the derivative of y for slope of tangent and normal line and then write their equations in…

Q: Find an equation for the line tangent to the curve y =x +1 at the point (-2,5). Sketch the curve and…

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

Q: Find the slope and equation of the tangent line to the graph of the equation at a given point. 1. y…

A: Given y = 2x² + 4x.     Point ( -2 , 0 ) To find slope & equation of tangent line.

Q: Find the equation of the tangent line to the curve y=9√x at the point (4,18). The equation of the…

A: Find y' and the value of y' is the slope for y.Find the slope m at (4,18).

Q: Find an equation of the tangent line to the curve at the given point. y = x3 − 2x + 2,    (4, 58)

A: Here we find the  equation of the tangent line to the centrey=x3-2x+2  at the point 4,58

Q: Find equations of the tangent lines to the curve y = (6 In(x)) at the points (1, 0) and at the point…

A: Solve by using equation of tangent

Q: find the equation of the curve passing through the point (0,2) and having slope x+ex-sinhx at point…

A: Given problem is : find the equation of the curve passing through the point (0,2) and having slope…

Q: Find the equation of the tangent line to the curve y=5x /1+x^2 at the point (4, 20/17) The equation…

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Q: Find an equation of the tangent line to the curve at the given point.   y= square root of 1-8x,…

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Q: Find equations of the tangent line and normal line to the given curve at the specified point. y =…

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Q: Find the equation of the tangent line to the curve y=8ln(x3 −63) at the point (4,0)

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Q: Find the equations of the two tangent lines to the graph of f that pass through the indicated point.…

A: f(x) = 2x − x2 We need to find the equation of two tangent lines to the graph of f that passes…

Q: Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)),  (2π, 0)

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Q: Find an equation of the tangent line to the curve at the given point. y = ln(x2 − 3x + 1),    (3,…

A: Given equation of curve y = ln(x2-3x+1)

Q: Find an equation of the tangent line to the curve at the given point. y = 2x3 − x2 + 3,  (2, 15)

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Q: Find equations of the tangent lines to the curve y = o mc) at the points (1, 0) and at the point (1,…

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Q: Find equations of the tangent line and normal line to the curve at the given point. y = x4 + 6ex,…

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Q: Find an equation of the tangent line to the curve y=3 arccos(x/2) at the point (1, pi

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Q: Find the point on the curve y=e3x where the tangent line passes through the origin

A: Given: y=e3x. let's that point on curve is a,e3a so, slopem of tangent is given by dydxa,e3a and…

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

Q: Find equations for the horizontal tangent lines to the curve y = x3 - 3x - 2. Also find equations…

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Q: Find an equation of the tangent line to the curve at the point (2, 0). y = ln(x2 − 3)

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Q: Find the point of the porabola y=x²-4x+3 where the tangent is parallel to the line 3x+y=2. Determine…

A: topic- equation of tangent line parallel to given line

Q: Find an equation for the line tangent to the curve y =x +5 at the point (2,9). Sketch the curve and…

A: Differentiating the equation of parabola and substituting the point gives the slope at that point.

Q: Find the equations of the two tangent lines to the graph of f that pass through the indicated point.…

A: Given function is fx=4x-x2

Q: Find an equation of the tangent line to the graph of the equation: x+y-ex-y=5 at the point (3,3)

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Q: Find the equation of the tangent line to the curve y = 2x +x-1 at the point (3, 20). %3D The…

A: The given curve is y=2x2+x-1. Find the equation of the tangent line to the curve y=2x2+x-1 at the…

Q: uation of the tangent line to the curve at the given point. = (1 + 2x)9, (0, 1)

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Q: Find an equation of the tangent line to the curve at the given point. y (4,16) (Express numbers in…

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

A: We have to find equation of tangent line

Q: Find the equation of the tangent line to the curve y = (x- 1)°(x+ 3)² at the point (2,25). The…

A: Firstly ,find the derivativw of y and then put the value of x coordinate of point to find the slope…

Q: Passing through the origin (0, 0), there are two lines tangent to the curve y =x + 1, one with…

A: Let (x, y) be the point of tangency on the given parabola. Hence, the tangent passes through the…

Q: Find an equation of the tangent line to the curve at the given point. x2 (4, 16) y (Express numbers…

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Q: Find equations of the tangent line and normal line to the given curve at the specified point. (1. )…

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Q: Find an equation of the tangent line to the curve at the given point. y = (x+1)/(x-8) ,    (7, −8)

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Q: The tangent line to a certain curve at any point P(x, y) has an x-intercept (not slope) equal to 3…

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Q: uestion 8 8. Estimate the slope of the tangent line to the curve y = -2x at x = -4, and then use it…

A: Equation of tangent line:  (y-y1)=m(x-x1) Slope of the tangent line on the curve at (x1,y1)=> m =…

Q: Find the equations of the tangent line and normal line to the curve y = x3- 2x 1+ at the point (0,…

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Q: Find the equations of the tangent line and the normal line of the function at the given value of x.…

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Q: Find the equation of the tangent line to the curve y=xlnx that is parallel to the line Y=1+3x.

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Q: Find equations of the two tangent lines to the graph of f(x) = 2x2 that pass through the point (1,…

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