a) The tangent line for y = f(z) at the point (c, f(e)) has as its equation y = f(c) + f'(e)(r – e). b) The two functions r(t) = t-Vi+sin² t+4 and €(t) = t3-t/2-cos?t+x have the same derivative. c) If f'(-n) exists then lim f(r) = f(-x). d) lim 840 e cot 0 1 does not exist.

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Q: 1. Find the equation of the tangent line to x2- 3xy +y2 = -1 at (2,1).

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: we have to find the slope of the tangent line to the graph of fx=sincos 2x at x=1

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Q: /4 Find an equation of the tangent line to the curve of y = sin2 x tan x at x 1

A: Consider the given curve.

Q: 5. Write the equation of the tangent line to the curve of y = e³x + cos(-x) at the point (0,2).

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Q: find an equation of the tangent line at the point specified. y = x3 + cos x, x = 0

A: Explanation: Given that,  y=x3+cosxand x=0   Calculation: Find the y-coordinate if x=0 Put x=0 into…

Q: 11.Determine the equation of the curve whose tangent line at any point (x,y) is e*-sin x and passes…

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Q: 18- What is equation of the tangent line of ƒ(x)=x³- 2x² - 1 at the point x = 2 ? y=-2x+9 1903…

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Q: Find an equation of the tangent line to the curve at thegiven point  y = ln ( x 2- 3x + 1 )       ,…

A: Given,y = ln (x2-3x+1)slope of tangent line is equal to the first derivative of curve at given point

Q: Find an equation of the tangent line at the given point.…

A: The given function is,x2+sin y=xy2+1 , (1,0)

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Q: Find an equation of the tangent line at the origin to the curve 1+ sin(x + y) = xy + cos y.

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Q: 3) Find the equation of the tangent line to the curve 6y³ – xy² + cos (xy) = 7 - at the point (…

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Q: 3. Find the equation of the tangent line to the curve x'y+y°x= 30 at point (1,3).

A: Solve the given problem.

Q: 5) Find an equation of the tangent line to the curve y = sin²(x) cos(x) at the point (,0).

A: Slope of tangent,m  = dy/dx Equation of tangent to curve at point (x,y) y -y1 = m (x -x1 )

Q: 34 10- Find equation of tangent line at the point (0, T) for Cos (7x- y) %3D 4y

A: Solved below

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A:

Q: Find an equation of the tangent line to ln(2x-y+1) + cos(xy-2)=1 at the point (1,2)

A: Given:

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Q: 3 Ay 10- Find equation of tangent line at the point (0, 7) for Cos (7x - y)

A: Solving

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Q: .2 Find the tangent line to y = x-x+2 at x=2.

A: Given - A function To find- Equation of tangent

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A: the equation of the tangent line at (x0 , y0) is y−y0 = m (x-x0)

Q: Find an equation of the tangent line at the point specified. y = x3 + cos x, x = 0

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Q: Find the equation for the tangent line to the curve f(x)=cos(x)-2sin(x) at the point (0,1). O y=-x+1…

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Q: 3. Find the equation of tangent line of the function f (x) = e" /x at the point æ 1. Write in the…

A: Given,  The function   fx = exx   We have to find the equation of the tangent line at the point x =…

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Q: 4. Find the equation of the tangent line to the curve 2xy+r sin y = 27 at the point (1.%).

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Q: 5. Determine the equation of the curve whose tangent line at any point (x, y) is e* – sinx and…

A: We need to find equation of curve.

Q: Find the equation of the tangent line at the given point. 4x = -5xy + 4y at (1,–4) y = arccos(5x) at…

A: See the calculation below

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

A: To find the equation of tangent to the curve given:

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A: topic - equation of tangent line to curve

Q: Find the equation of the tangent line to the curve 2y³ – xy² + cos (xy) = 3 at the point ( 0,1) .

A: Given curve is:  2y3-xy2+cos(xy) = 3 For slope of the tangent, differentiate the curve equation

Q: 7. Find all x-coordinates where the tangent line to y = f(x) = sin(2x) – cos?(2x) is horizontal. -

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Q: Find the slope of the tangent line to x2y2+x sin (15y) = 4 at any point, (x,y) on the curve.

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Q: 1. Find the equation of the tangent line to x² – 3xy + y² = -1 at (2,1).

A: given that x2-3xy+y2=-1slope of tangent (m)= dydxdifferntiate the given curve with respect to…

Q: Find the equation of the tangent line to the curve: sin (2x + y) + cos-'(x +2y) 6 at the point Enter…

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Q: 2. Find the equation of the tangent line to the graph of 3x cos y = 1 + x² + /2y+ 1 at P(1,0).

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Q: Find an equation of the tangent line to the curve at the given point. y = cos (x² – 2x + 1), (1, 1).

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Q: Find the equation of the tangent line to the curve a(x) = 3 sin-x+ In(x² – 5x +1) – e**-6x at x = 0

A: Point -slope form : y-y1=m(x-x1) ; where 'm' is slope and (x1,y1) given point.

Q: Find a formula for the tangent line for y = sin(x) cos(x) at x = 4 -

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Q: 1- Find the equation of the tangent to the curve y= 2 sin x+ cos2x at the point x = n. 2- Find the…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: The slope of the tangent line to the curve 2xy + T cos y = 2n at point (1,“) is:

A: The given equation is 2xy+π cos y=2π and the point is 1, π2. Evaluate the slope  y' using implicit…