Find the points at which the graph of the equation has a vertical or horizontal tangent line.        4x2 + y2 − 8x + 4y + 4 = 0

Q: C. Find the slope and the equation of the tangent line to the curve. 1. у %3D х2- 4х + 1 at (2, -3)

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Q: Find an equation of the line tangent to each of the following curve at the given point. y + Vxy = 6;…

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Q: Find ​(a) the slope of the curve at the given point​ P, and ​(b) an equation of the tangent line at…

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Q: Find an equation in the form y = ax? + bx + c whose graph has an x-intercept at x = -1 and a tangent…

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Q: Find the points at which the graph of this equations has vertical or horizontal tangent lines:…

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Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

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

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Q: find (a) the slopeof the curve at the given point P, and (b) an equation of the tangentline at P. y…

A: a). Slope of the curve is the derivative of the curve at the given point. So differentiating given…

Q: Find the equation of the tangent line to the curve y = 5sec(x) -10cos(x) at the point (pi/3,5).…

A: Given query is to find the equation of the tangent.

Q: Determine an equation of the line tangent to the curve at the given point. 4x² + 4xy + 3y 51, (3,1)

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Q: Consider the following equation. 4x3 + 3y2 = 52 Step 2 of 2: Find the slope of the tangent line at…

A: The given equation is 4x3+3y2=52. Evaluate dydx using implicit differentiation as follows.…

Q: Find an equation for the tangent line to the curve defined by the equation ?x^2y^2+ xy + y = 1 at…

A: Given: x2y2+xy+y-1=0 for finding equation of tangent for given curve at given point, we need to find…

Q: find (a) the slopeof the curve at the given point P, and (b) an equation of the tangentline at P. y…

A: Given curve:

Q: Find an equation of the line tangent to the given curve at a. y = x3 – 4x2 + 2x – 1; a = 2

A: Slope m of the tangent will be given by dydx Therefore, dydx=ddxx3-4x2+2x-1 ⇒dydx=3x2-8x+x…

Q: find the equation of the line tangent to the curve at the given point x2y2=4y ;(2,1)

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Q: Find the slopes and equations of the lines tangent to y = f(x) at the given point.

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Q: Find an equation of the tangent line to the parabola at the given point. y 15 10 x² = 8 y (7, 49/8)…

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Q: Find an equation of the tangent line to the graph at the given point. (y - 3)² = 4(x - 5), (6,5) ||…

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Q: Find an equation of the tangent line to the parabola y = x2at the point (2, 4).

A: To find the equation of the tangent line to the parabola y = x2at the point (2, 4). For the parabola…

Q: Find the slope of a line tangent to the curve of the given equation at the given point. y=(x^3)/4;…

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Q: Find an equation of the line tangent to each of the following curves at the given point. x2y + y3 =…

A: Given Data : Equation of Curve x2y+y3=5 To Find: Equation of line tangent to the curve at 12,12 The…

Q: The equation of the tangent line to the curve at the given point. x2 v2 2-13 = (1, 1) is %3D 100 4…

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Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: Given: y=5x2+4 ; P3,49 we know that slope at given point 3,49 is given by y'3 so, for finding slope…

Q: find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the point(s) on the graph of the following equation that have horizontal or vertical tangent…

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Q: Find the slope of the tangent to the curve y = 3e^(2x) at (0,3)  a. 3  b. 2  c. 6  d. 12

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Q: (b) Find the points on the curve y = 2x3 – 3x2 – 12x + 20 where the tangent is parallel to the…

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Q: Find the equation for the tangent to the curve y = exp [6x] at the point (7, e 294). f(x) = exp…

A: given: the equation of the function is: y=e6x2 the given point is: 7,e294

Q: Given the curve y= x^3 - 4x +1 . Find the equation of the tangent at the points where the slope of…

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

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Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,  (−9,81/2)

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Q: Find an equation of the line tangent to each of the following curves at the given point. 4x 11, 12 y…

A: The given equation of curve is y=4xx2+3                  ……(1) Now differentiate the equation (1)…

Q: Find an equation for the tangent to the curve at the given point. y = x2 - 4, (2,0) О А. у32х- 8 В.…

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Q: Given that x² + y? = (2x² + 2y² – x²)? Find an equation of tangent line to the curve at point (0,…

A: The formula to differentiate the product of two functions, f(x) and g(x) with a common variable is…

Q: Find the equation of the curve whose slope at any point is In and which xy2 passes through the point…

A: Point (x1 , y1) = (1, -2) Slope = ln1xyxy2

Q: find the equation of the line TANGENT of the given curve for x=pi/6 y=5cos(2x)

A: Explanation of the answer is as follows

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 25x2 +…

A: 16y2+200x-160y+400=0 Differentiating with respect to x implicitly 50x+32ydydx+200-160dydx+0=0…

Q: 7x Find the points on the graph y = x-2 - where the slope of the tangent line is parallel 28x +50y –…

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Q: If y = x* - 4x° - 8x², the points at which the tangent to the curve is parallel to the x-axis are A.…

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 16x2 +…

A: Solution of given question is written in below steps.

Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = −1 and B ′(24) =…

A: Given thaty=B24 x=24y=B24 =-1B'24 =-14To :find equation of tangent line Solution :equation of line…

Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

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Q: For what value or values of the constant k will the curve y = x3 + kx2 + 3x - 4 have exactly one…

A: Given curve is y=x3+kx2+3x-4. A curve have exactly one horizontal tangent  at x=a if f'a=0.…

Q: Determine the equation of the tangent to the graph of the equation xy – 2x'y-3ry + 5y – 4 = 0 at the…

A: To find the equation of tangent to the given equation at (1,2).

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

A: By using slope formula and equation of tangent line, we find the required equation of tangent line.

Q: Find the equation of a tangent line that is tangent to the graph as stated below 3x 5y = -17 at (-1…

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Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: Equation of tangent to a curve y=f(x) at a point (x0,y0) is y-y0=f'(x0)(x-x0)

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

A: use property of chain rule to find the slope and equation of tangent line

Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = 0 and B'(24) = -…

A: Given,         y=Bx at x=24 if B24=0 and B'24=-14.

Q: Find the equation of the curve at every point of which the tangent line has a slope of 4.r. (a) (h)…

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Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: