Find the equations of the tangent line and normal lines to the graph of the function f(x) = 3 sin x at x = T/2. a) Tangent line: |y =v b) Normal line: x = v

Q: Determine the slope of the tangent line to the curve of sin(x + y) = y2cos(x)  at  the point (x,y) =…

A: Topic = Derivative

Q: Find an equation of the tangent line to the graph of y=x at the point where x=e. ... The equation of…

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

Q: At what points (r, 0) on this curve are the tangent lines horizontal? Use 0 < 0 < 2n. r = 1- sin 0

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Q: find an equation of the tangent line to f(x)=3 cos(x) at x=2pi/3 Let y=f(x) and express the…

A: At x=2π3, f(x)=3cos(x)f2π3=3cos2π3f2π3=-32So, the point is 2π3,-32

Q: Find the slope of the tangent line to the curve 6 sin(x) + 2 cos(y) – 4 sin(x) cos(y) + x = 3T at…

A: We have to find the slope of the tangent line to the curve…

Q: Show that the tangent lines to the curve y = (pai sin x)/x at x = pai and x = -p ai intersect at…

A: Given:

Q: (a) Find the equation of the tangent line to the curvey = 2 sec x – 4 cos x at the point (, 2) %3D

A: Note: -Since you have asked multiple questions, we will solve the first question for you. If you…

Q: (a) Find the equation of the tangent line to the curvey 2 sec x- 4 cos x at the point , 2) %3D

A: Since you have posted a multiple  question according to guildlines I will solve first…

Q: Find the equation of the tangent line to y = x + tan (x) where x = TI.

A: We have to find the equation of tangent line .

Q: A curve is defined by y=(1/3)sin(2x+1). Evaluate the angle between the tangent to the curve at x=2,…

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Q: Where does sin x have a horizontal tangent line? Where does cos xhave a value of zero? Explain the…

A: Concept: The function f(x) at the point x=a, is a line that just touches the graph of the function…

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

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Q: Find the slope of the tangent line to the sine function at the origin, (a) y = sin(4x) 15 y'(0) = 4…

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

A: Given: y=sec(x)-2cos(x)

Q: Show that the tangent line to the graph of y = ex at the point (a, ea) is perpendicular to the…

A: Given: y=ex  ……1 Tangent line, with slope say m1, of above equation passes through a, ea.   Also,…

Q: 2. Let f(x) tan (2) at the point (1, 7)? tan (r). What is an equation to the tangent line to y

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Q: find an equation of the tangent line at the point specified. y = sin x + 3 cos x, x = 0

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Q: (플아 What is the equation of the line tangent to the curve e + cos(x) = 1 at the point ,0?

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Q: 3. Find the equations of the tangent and normal lines to the curve f(x) = /2* +cos(x*) at(0,/2).…

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Q: Find an equation of the tangent line to the graph of y x at the point where x e. .... The equation…

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Q: Find the equation of the tangent line to the graph of the equation sin "(a + v) = - at the point (1,…

A: Tangent line to the curve

Q: Show that the tangent lines to the curve y = (π sin x)/x at x = π and x = -π intersect at right…

A: The equation of the curve is y=πsinxx

Q: Find the slope of the tangent line to the curve 5 sin(æ) + 3 cos(y) – 4 sin(x) cos(y) + x = 7n at…

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Q: Find an equation of the tangent line to the curve at the given point. sin(sin(x)), (37, 0) y

A: The given expression is,

Q: Find the slope of the tangent line to the curve y=Xarcc sin x at the point 2, Ta

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Q: Estimate sin (31) using an appropriate tangent line to the graph of y = sin(x).

A: Consider the provided question, We need to estimate sin31° by using tangent line to the graph of…

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

A: The given paramedic equations are,

Q: 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: Find the equation of the tangent line for f(x)=sin-1(1/4x) at the point (2,pi/6).

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Q: Let y= 3 cos x-5 cot x+ csc x tan x, then the slope of the tangent line at x = is 4

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

A: To find the equation of tangent line at the given point.

Q: A Find the slope of the tangent line to ya fix) = 1+x+x2 at X=a. %3D

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Q: Find an equation of the tangent line to the curve at the given point. y = sin(sin r), (3T, 0) y =

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

A: Given equationy=sec(x)-2cos(x), P=π3,1To calculate the tangent line we have to calculate the slope…

Q: Let point E lie in the exterior of OP. How many tangent lines can be constructed to OP from point E?

A: two tangent line can be drawn to a circle from a point E outside of the circle.

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 all points on the graph of ƒ(x) = 2 sin x + sin?x where the tangent line is horizontal

A: f(x)=2 sin x+sin2x

Q: Find points of horizontal and vertical tangent lines r = 1- cos(0) %3|

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Q: (b) Find the equation of the tangent line to the graph of the equation sin-"(x + y) = 5* 2 at the…

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Q: Find the slope of the tangent line to the curve 5 sin(z) + 4 cos(y)- 5 sin(z) cos(y) + z = 3x at the…

A: Consider the curve  5sinx+4cosy−5sinxcosy+x=3π

Q: Find an equation of the tangent line to the y = sec(x) – 6 cos(x), P = 3 y =

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Q: Find all points the graph of f(x) = 2 sin x + sin?x where the tangent line is horizontal on

A: Solved below

Q: Find an equation of the line that is tangent to the curve y = e* sin x at the point (0, 0). Tangent…

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Q: 1. Given y = sin(x In.x), what is the slope of the tangent line at (e, 0)? (The red line.) 2. Given…

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Q: Find the equation of the tangent line to the curve y 6x cos x at the point (π, = The equation of…

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Q: (a) Find the equation of the tangent line to the curvey 2 sec x – 4 cos x at the point (÷, 2)

A: Tangent line to the curve y=f(x), where f(x) is a function of x at point x0, y0is given by:…

Q: Show complete solution. Determine the slope of the tangent line to the graph of the equation ey =…

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