The following graph shows g(x) and consists of a line, semicircle with radius 2, and two horizontal lines. Find the value of ſ°, g(x)dx. Show your work.

Q: For what value of x does the graph of y = eš (4x – 5)° have a horizontal tangent line? -

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Q: C. If h(x) = [f(x)]² + g(x),what is the equation of the line tangent to the graph of h at x = -2?…

A: First we will find derivative of h(x) at x=(-2) that gives the slope of the required tangent.

Q: Find the equation of the image when y = -x+2 is reduced with scale factor of 2/3 centered at (1 ,…

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Q: Start with the graph of y = ln x. Find an equation of the graph thatresults from reflecting about…

A: If a function is reflected over the y=x line then (x,y) → (y,x) This means y=ln(x) will become…

Q: Find the equation(s) of the tangent line(s)to the graph of the parabola y = x2 through the given…

A: Given, y=x2

Q: h (x) = [ƒ (x)P + g (x), what is the equation of the line tangent to the graph of h at x=-1?

A: Given,           hx=fx2+gx

Q: Find the area A of the largest rectangle that can be inscribed under the curve of the equation below…

A: Given y=e-x2

Q: For what values of a are the graphs of y = a* and y = 1 +x tangent at x = 0? Enter the exact answer.

A: Please see the explanation below

Q: If the graph of Y=f{X) contains the point (0,2), dy dx and f(X) > 0 for all X, then yet? f(x) =

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Q: By experimentation, determine the approximate value of a (where 3 < a < 4) at which the graph…

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Q: Assume y = 3 · 5* is the equation for the blue line shown in the graph below, and that the black…

A: The equation of curve is:  y=3·5x

Q: For what value(s) of x does the graph of f(x) = 6x³ + 9x² – 216x %3D e a horizontal tangent?

A: To find the values of x does the graph of fx=6x3+9x2-216x have a horizontal tangent.

Q: (i) Find the values of k for which y= kx + 2 is a tangent to the curve y= 4x2+ 2x + 3.

A: If y = kx +2 is tangent to the curve y=4x2+2x+3, then the point of intersection of the line and the…

Q: Use the graph to answer the following questions? (see the graph as attahced )   Estimate the…

A: Consider the curve    y3−9y2+27y+5x2=47

Q: The curve C with equation y = f(x) passes through the point (1, -3). Given the following, find f(x)…

A: We know, ∫xndx= x(n+1)/(n+1)

Q: 56. For what value of a does the graph of f (x) = e® – 2x have a horizontal tangent?

A: Given query is to find the value of x where tangent is horizontal.

Q: Find the point P on the graph of the function y = yx closest to the point (4,0 The x coordinate of P…

A: Given that, graph of function  y=x   We have to find Point P on y which is closest to (4,0)

Q: Find the point P on the graph of the function y = Vx closest to the point (3,0) The a coordinate of…

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Q: Use the graph to answer the following questions? (see the graph as attahced ) Estimate the point(s)…

A: We have given a graph of a function .  We have to estimate the point(s) where the graph has a…

Q: The line y = 2x + b is tangent to the graph of y = 1x at the point P = (a, 1a). Find P and determine…

A: Given: The line y=2x+b is tangent to the graph of y=x at the point Pa,a. To find P and determine b.…

Q: 50 Find the length of the curve whose equation is given by r = e on 0 < 0 < 2T.

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Q: Q6. Find the equation of the tangent line to the graph f(x)=2xsinx at x=n

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Q: The point (2,1) is on the graph of x2 . y3 + 5· x² = y² + 23. Find the slope of the line tangent to…

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Q: sec(2x+π) eq

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Q: Given that f(2) = -5 and f'(2) = 3, find an equation for the tangent line to the graph of y = f(x)…

A: we have to find equation of tangent line

Q: For what values of x does the graph of f(x) = 2a – 9a? – 60x – 3 have a horizontal tangent line?…

A: Given function is fx=2x3-9x2-60x-3. Compute the derivative. f'x=2x3-9x2-60x-3'=6x2-18x-60

Q: Find an equation of the tangent line to the curve

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Q: given x3   + y3 -9xy = 0,   find the point where the curve has a vertical tangent line

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Q: Given that f(−6)=−6 and f′(−6)=−6, find an equation for the tangent line to the graph of y=f(x) at…

A: We know that slope of tangent line to the graph of y=f(x) at x=a is f'(a) Therefore, slope of…

Q: Consider the following. x1/2 + yl/2 = 8 dy Find dx () dy Find the slope of the graph of the equation…

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Q: 2 For the graph of f(x) = ax + bx +4, the slope of the tangent at the point (3, 1) is 5. Determine…

A: Given that        f(x) = ax2+bx+4

Q: The graph of y=a3x2+a2​, where a is a constant is called the witch of Agnesi.   a. Let a=6 and find…

A: a). Given, y=216x2+36 Differentiating with respect to x, we get…

Q: Start with the graph of y = ln x. Find an equation of the graph thatresults from reflecting about…

A: Given: y=lnx equation of the graph that reflecting about y-axis will be y=ln-x

Q: Given the cosecant functions of y=csc(x/2-π/2) find the equation of all of its vertical asymptote

A: We know that the Cosecant function only has vertical asymptotes. It does not have any horizontal…

Q: We are given f(x) = 9x2 and f '(x) = 18x. Find the slope of the tangent to the graph of  y = f(x) at…

A: Given,

Q: Find an equation of the tangent to the curve at the given point. x 3 , y = t2 3, (3, 4)

A: Given curve is

Q: The graph of y = fx) and the tangent to the curve at x = 1 is shown below. ..... 5 3 y - f(x) -1 0.

A: Consider the given figure.

Q: Given x +y' - 3y = 4 a) At what value(s) of x does the graph have a horizontal tangent? b) At what…

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Q: Find the point(s) on the graph (x- 1)2+ (y +3)² = 16 where t tangents are horizontal.

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Q: h(x) * |4x + 1 %3D a) Find the equation of the line tangent to the graph of fx) at x = 2.

A: 8). Given function is hx=4x+1. To find: (a). The equation of the line tangent to the graph of fx at…

Q: Choose the correct graph of y = sin x, -"sxS T: 1 -37 21 -1 -2

A: The given function is: y=sin x ;                 -3π2≤x≤π

Q: fa is a positive integer, then the slope of the tangent to the graph of y = a²a - aln(ax + 1) at a =…

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Q: Does the graph of S0, x< 0 U(x) = 1, x2 0 have a vertical tangent line at the point (0, 1)? your…

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Q: Sketch the graph of h(t) = |t| + |t + 1|

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Q: Estimate the slope b t the pótst a,where *3 9. X= 2 feck)- Estimate the arca above the x-asxis and…

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Q: Choose the correct graph of y = sin x, - T < x < 2 T; and y = csc x, - T < X< 2T: 2 1 27 -1 -2

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Q: The range of y = sec x is ________.

A: The range of y = sec x is ________.   Cosine function only takes values that are between -1 and +1.…

Q: Sketch the graph of y = t + sin t for 0 ≤ t ≤ 2π.

A: The given function is y=t+sin t    for  0≤t≤2π. Sketch the graph of the above function as shown…