Find the equation of the curve y = f(x) as shown in the figure with line tangent to curve at P(x , y) and the tangent line intersects the y-axis at 4.

Q: Find an equation of the tangent line to the graph of the equation In(x) + xe' = 1 at the point (1,…

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Q: (a) Differentiate with respect to x: g(x) = 4x2 – x +5 (b) Differentiate with respect to x: h(x) =…

A: We know that :ddxf(g(x))=f'(g(x))g'(x)

Q: 16. Find the equation of the tangent line to the curve y = e* at the point (a, f(a)) when a = In 3.

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: FInd an equation of the line that is tangent to the curve y=e^xcos(x) at the point (0,1).

A: The equation of the curve is y = e^x(cos(x)) and the point is (0, 1). Differentiate the function…

Q: 1. Find the equation of the tangent line to the curve: x = = VE, y = et %3D at t=1.

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Q: use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an…

A: Given, y=2-x3 Point P = (1, 1)

Q: b. b. y = 2 1+e-x at (0,1)

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Q: The curve y = x /( 1+ x2 ) is called a serpentine. Findan equation of the tangent line to this…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: Explanation of the answer is as follows

Q: Find an equation of the tangent line at a point (0, 0) on the curve x =t- 100, y = t2– 10t.

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Q: Find an equation of the line tangent to the curve y = e at (0,1). 2x

A: We need to find the equation of tangent to the curve: y=e2x  at (0, 1) This can be done as follows:

Q: Find the equation of the tangent line to the graph xy^2 − 2y = x^2 at the point (2, −1).

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Q: Find an equation of the tangent line to the given curve at the specified point. x² - 1 y = (1, 0) "…

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Q: Find an equation of the tangent line to the curve at the given point. y = Vx, (64, 8)

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

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Q: Find an equation of the tangent line to the curve at the given point. y = Vx, (1, 1)

A: Given: To find an equation of the tangent line to the curvey=x at the given point (1,1)

Q: Find the slope and the equation of the tangent line to the given curve at the point corresponding to…

A: The solution are next step

Q: Find the equation of the tangent line at the given point on the curve. 2y- Vx 28, (16,4) y=D

A: 2y2-x=28,    16, 4. Slope of the tangent line is the derivative of the given function at the given…

Q: Find an equation of the tangent to the curve  y= x ln x at the point (e ,e )

A: Given: y=xlnx, e,e for finding equation of tangent, we need slopem of tangent at given pointe,e we…

Q: Find an equation of the tangent line to the curve at thegiven point  y =  e x  / x…

A: Given curve is y=exx To find: Equation of the tangent line to the curve at point (1,e). Solution:…

Q: Find an equation for the tangent curve x= 3e^t, y= 5e^-t at t = 0.

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Q: 4. Find the equation of the tangent to the curve y = xe* at the point (1, e):

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Q: Find an equation of the line tangent to the graph of y sin x – 3y = 4 at the point %3D (, 4) .

A: y2sinx - 3y = 4 at (π/2 , 4) we have to find slope of function 2ysinx(dy/dx) + y2cosx -3dy/dx = 4…

Q: Find the equation of the tangent line to the curve at the given point. y = 9x – 8/x, (1, 1) %3D

A: Given,           Equation of the curve is y = 9x -8x  and point = (1,1)

Q: Find the equation of the tangent line to the curve y = 6 sin x at the point (T/6, 3).

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Q: Find an equation of the tangent line to the curve at the given point

A: We have given the curve y = x5 + 3e5 and the point (0, 3). Find the slope at x = 0. Therefore, we…

Q: 3. Find the equation of the tangent to the curve 3xy-y²= 7 at the point (.1).

A: Follow the procedure given below.

Q: 3. Find the equation of tangent line to the curve 2x – y + 3 = 0 x = t – 1, y = t³ + 1 parallel to…

A: Equation of tangent line is given by- y - y1  = m (x - x1)

Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

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Q: Find the slope of the tangent line to the curve (r² + y² – 1)3 – r²y³ = 0 at the point (–1,1).

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Q: Find an equation of the curve y = f(x) if y^n = 6x and the tangent line to the curve at (1, 2) is…

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Q: II. Find the equation of the tangent line to the curve z2+V#j+y² = 19 at the point (1, 4).

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: 1. Find an equation of the tangent line to the curve y = Vx at the point (1, 1).

A: Question no. 1Given,            A n equation of the tangent line to the curve y=x at the point…

Q: Consider the curve given by y2 + (1+x³)3 = xy + 8. Find the equation of the tangent line to the…

A: To find the equation of line tangent to the given curve at point (1,1)

Q: Find an equation of the tangent line to the curve y= e* that is parallel to the line y=1-2x.

A: Two parallel lines have the same slope

Q: Find the equation of the tangent line to the curve y = = tan x at the point (T/4, 1). y =

A: We know that slope of line is : m = dy/dx at x=a. And equations of line is if slope is given and…

Q: 3. Find the equation of the tangent line at point P(2,1) to the graph of the curve f(x) = v3x – 5

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Q: Find the equation of the tangent plane to the graph of f(x, y) =−3x2 − y3 at the point (x, y) = (2,…

A: The given function is

Q: find the equation of the tangent lines to the curve y=2/(1-3X) at the points with x-coordinates 0…

A: Find the y- values for the given values of x.

Q: Find the equation of the tangent line on the curve defined by 2xy - y2 = 1 at x = 1. a. y = 1 b. y…

A: To determine : The equation of the tangent line on the curve defined by 2 x y - y 2 = 1   at   x =…

Q: Find an equation of the tangent line to the curve at the point (1, 1/e)   y = x3e−x

A: Given query is to find the equation of tangent line to the curve   y = x3e-x

Q: Find the equation of the tangent line to the curve x=4+2t, y=1−t2 at the point t=1.

A: We need to find the equation of tangent line to the curve at point t=1

Q: B) Find the slope of the line tangent to the curve y = sin x at the point where x =

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Q: Consider the curve given by y2 + (1+x³)³ = xy + 10. Find the equation of the tangent line to the…

A: Considering the curve- y2+1+x33=xy+10 Firstly, find the slope of the curve. dy/dx is the slope of…

Q: Find the point where the tangent line to y = a" at a = 0.6 crosses the x-axis. x-intercept =

A: X- intercept is x=0.45 See the calculation below

Q: The equation of the tangent line to the curve y=x² +1 at x = -4

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Q: Find the equation of the tangent line of the curve y = sin x + cos x at the point A(, v2). 4'

A: Point-Slope form of equation of line : y-y1 = mx-x1 where m is the slope of the line and x1, y1 is…

Q: Q3) Find the equation of tangent line to the curve y/sin(x) +y²=2 at the point (,1).

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Q: Find the equation of the tangent line to the curve xy +xy 12 al the point (6, 1).

A: