Find an equation of the line tangent to the given curve at x =a. Use a graphing utility to graph the curve and the tangent line on the same set of axes. y =9+ 2x + 4x e X; a= 0

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 the slope of the tangent to the curve. (If an answer is undefined, enter UNDEFINED.) x2 + 2xy…

A: Given, x²+2xy+5= 0 Differentiating w.r.t x we have, dx²/dx + d(2xy)/dx +d(5)/dx= 0 2x+ 2y.dx/dx +…

Q: For what value of x is the tangent line to the curve y= x2 – 6x+5 horizontal? A В -6 3 D -3 E none…

A: Given y=x2-6x+5

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, A curve y=x12  and a point P(4,2) (a). To find the slope of the curve a the point P (b). To…

Q: Find an equation of the tangent line to the graph at the given point. x?y2 - 9x² – 4y² = 0, (4, 2/3)

A: Given equation of function:

Q: Find an equation for the tangent to the curve at the given point. 19) f(x) = 10/x - x + 7, (100, 7)…

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Q: Find an equation of the line tangent to the given curve at x=a. Use a graphing utility to graph the…

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Q: find the slope of the line tangent to thegraph of ƒ at P.b. Determine an equation of the tangent…

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Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the…

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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…

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Q: Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the…

A: Given

Q: In (r? – 3) + e?-² at the 1. Find an equation of the tangent line to the graph of y = point (2, 1).

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Q: For what value of x is the tangent line to the curve y= x² – 6x +5 horizontal? (A -3 3 D none of the…

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Q: Find the equation for the tangent to the curve y= exp 5x] at the f(x) = exp [5x?] The equation for…

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Q: find the slope of the line tangent to thegraph of ƒ at P.b. Determine an equation of the tangent…

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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=1-5x2, P(2,-19)

Q: Consider the following curve. y = 3x2 – 11x + 1 Find the slope m of the tangent line at the point…

A: Given that: Equation of curve is: y=3x2-11x+1        and point on the curve is (4,5)

Q: 3. Find the equation of the curve at every point of which the tangent line has a slope of 4.x. (a) y…

A: Slope = dy/dx

Q: Solve the following. Show the step-by-step solution. 1. Find the equation of the tangent line and…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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: Find y' and the slope of the tangent line to the graph of the equation below at the indicated point.…

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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 the slope of the line tangent tangent to the graph a the given poin 4 y = ,x = 6 5+x 4 m = 121…

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Q: (a) Find an equation of the tangent line to the curve y = 14/(1 + e*) at the point (0, 7).

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Q: The slope of the tangent line at any point (x. y) on a curve is 2x. If the point (9, 3) is on the…

A: the slope of the curve is the derivative of the function at that point.' here we have to form a…

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: Determine the equation of the tangent to y = (x – 7)(x+2) at the point P(-1,-8). Answer:

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Q: Determine the equation of the curve for which the tangent line at every point has a slope of 25, x =…

A: Topic = Coordinate geometry Correct option = D

Q: tind the equation op the tangent line to the graph of tG) 5 at point at which x=0. . 2x-1

A: The given function is  f(x) = y = (x - 5)/(2x - 1) The given point x = 0 y = (0-5)/(2*0-1) y = -…

Q: (a) Find the slope of the curve at point P and write the equation of tangent line at point P. 2x? –…

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Q: 6x Find an equation of the tangent line to the graph of y = 2 X +1 at the origin and at the point…

A: Given,          The line is y=6xx2+1 at the origin and at the point -1,-3.To find : Find an equation…

Q: For what value of x is the tangent line to the curve y= x² – 6x +5 horizontal? (A none of the given…

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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 slope of the line tangent to thegraph of ƒ at P.b. Determine an equation of the tangent…

A: (a) we have to find the slope of the tangent to the graph of f at P. f(x)=1x  ,…

Q: A curve is given implicitly by the following equation .2 (x + y)² + x²y = 11 Find the slope of the…

A: Given the equation of the curve is  x+y2 + x2y = 11

Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the…

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Q: Find an equation of the tangent line to the graph at the given point. x?y² - 9x² – 4y² = 0, (4, 2/3)…

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Q: A) Find an equation of the line tangent to the function of x? + (y - x)? = 9 atx = 1.

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Q: EX Find the equation of the tangent Line to the curve y=x? at c 204)

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Q: For what value of x is the tangent line to the curve y= x2 - 6x +5 horizontal? A -6 B -3 (D 3 (E)…

A: We know that a horizontal tengent line have slope zero or first derivative is equal to zero . Given…

Q: Ql: Find an equation for the tangent to the curve at the given point. 1.y=2V (1,2)

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Q: find the slope of the line tangent to thegraph of ƒ at P.b. Determine an equation of the tangent…

A: Given information: The function is ƒ(x)=3x + 3 and the point is P(2,3). (a) To find: The slope of…

Q: k(x) = |x – 1| at x = -15

A: k(x)=x-1 at x=-15

Q: Find the equation of the tangent line at the point (a,f(a)). Sketch the graph and the tangent line…

A: To find the equation of the tangent line at the point (a,f(a)).

Q: For what value of x is the tangent line to the curve y= x2 -6x +5 horizonta? A -3 B C) none of the…

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Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the…

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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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Q: find an equation for the tangent line to the curve atthe given point. Then sketch the curve and…

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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: