1. Sketch the curve by following the guidelines: a) domain, b) intercepts, c) symmetry, d) asymptotes, e) monotonicity, f) local extreme values, g) concavity and inflection points, h) sketch the curve. f(x) = (1– x)e*

Q: Find an equation of the tangent to the circle x2+y2=36 at the point (5,3)

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Q: In  the givne equation as follows ,determine the open t-intervals on which the curve is concave…

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Q: Let the curve C be the mirror image of the parabola y" the line x+y + 4 = 0 If A and B are the…

A: Given: Parabola:y2=4xLine:x+y+4=0   A and B are the points of intersection of C with the line y=−5…

Q: Construct a smooth curve tangent to the line segments starting at point P. P

A: Given: a group of line segments joining to form a zig-zag figure. Aim to form a curve which is…

Q: Use the guidelines to sketch the curve  y = 2 x2  / ( x 2  -1 )

A: For, x=0, y=0  So, the y-intercept is 0   Then we plug y=0 and find x so, x-intercept is 0.

Q: How do I do this?

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Q: Explain the steps required to find the length of a curve y = ƒ1x2 between x = a and x = b.

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Q: Use the curve sketching guidelines to sketch the following curve. f(z) = (4 – 2)5 %3D Domain:…

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Q: Determine the length of the tangent to the circle x2 + y2 − 4x − 5 = 0 from (8, −2)

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Q: Consider the accompanying graphs of y = 2x + 3 and y = In x. Determine the %3D a. minimum vertical…

A: (a) Given information:

Q: sketch the domain of f(x,y) = sqrt(x^2-y) and describe the level curve

A: Domain of a function is the collection of all values that go into a function. A level curve of a…

Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y=…

A: A) 4 B) 6.28 C) -35/2  ( mark limit is given from 0 to 7)

Q: Find the equation of the hyper bola with latus rectum 1, slope of asymptotes +- 1/2. Draw the curve.

A: Consider the general form of the hyperbola is, x2a2-y2b2=1 Since, the latus rectum is 1 then,…

Q: Show that the curve y =(1 + x)/(1 + x2) has threepoints of inflection and they all lie on one…

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Q: Find the exact length of the curve. 1 y = 4 -x² - In(x), 1< x < 8 2

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Q: 1 - Sketch the curve : y=-(x3– 6x²+9x+6). 6 y=Lcx³-

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Q: Find the exact length af te of the curve, 2. x-

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Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y

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Q: (x – 2)2 + y² = c² %3D

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Q: Use the guidelines of this section to sketch the curve   y =2 x- tan x  ,  - pie/2&lt;x &lt;pie /2

A: Given: Differentiate the above expression and equate to zero to find the local minima and local…

Q: Find the exact length of the curve. 는x - - In(x), 1<x<6 4 2

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Q: find the Po s at which the tang ent liae to the graph of funstion S)= x3-4x+ 5o has Slope equalta 30

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Q: y= In x

A: Given function is y=x/ln(x)

Q: (1) Find a point P in the first quadrant on the curve f(x) = such that the rectangle with sides on…

A: In the question we have to find the perimeter of the rectangle.

Q: Prove that the curves y2 = 4x and y2-6x+1 = 0 touch each other at the point (1,2)

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Q: ) Prove that the Point P(!,-) is a minimum Point of the curve y =lnx

A: Any point (x,y) is minimum for a given curve if it satisfies below two condition, a) First…

Q: Find the member of the curve whose slope at any point is 2e** and passes through the point (0, 1)

A: We need to find the member of the curve whose slope at any point is 2e^(4x) and passes through…

Q: Find the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

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Q: Use the guideline of this section to sketch the curve 1. y = 1 + 1/x + 1/(x ^ 2)

A: To Sketch: y=1+1x+1x2 Explanation: (a). Domain and Range y=1+1x+1x2is defined everywhere except…

Q: Find the length of the tangent to the circle x²+y²-2x-3y-1=0 from the point (2,5).

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Q: Explain why a cubic Bézier curve is completely determined by x(0), x (0), х(1), and x'(1).

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Q: Exercise 1.2.16 Find the circle x2 +y² +ax+by+c=0 passing through the following points.

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Q: Find the length of the tangent to the circle x² + y² − 2x − 3y − 1 = 0 from the point (2, 5)

A: Solution- The equation of the circle x2+y2-2x-3y-1=0 The point =2,5 length of the tangent

Q: Find the exact length of the curve. 1 x² -In(x), 1< x < 8 4

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Q: Sketch the curve with equation x2/3 + y2/3 = 4 and use symmetry to find its length.

A: Arc Length formula in the interval [a,b] is given by, L=∫ab1+dydx2 dx This is applied only when dydx…

Q: Compute the equation of the horizontal asymptote of the curve y = (2x- 1)/ (x + 2). y = 2 x = 2 X =…

A: Given; y=2x-1x+2   As we know that; To calculate the horizontal asymptote, solve the limit…

Q: 2. Use the guidelines to sketch the curve. Y In x x²

A: The given function is: y=ln xx2 Note that the domain of the function is (0,∞). First of all, let's…

Q: 3- Find the length of the curves in Exercises 1-4. X = (y3/2/3) - y¹/2 from y = 1 to y = 9

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Q: At what part of the curve 2x2 + y? = 8 does it assume the highest value?

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Q: Sketch the curve with equation  x2/3 + y2/3 = 1  and use symmetry to find its length.

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Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

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Q: Find the exact length of the curve. 1 y = -x° 4 x² -- In(x), 1<x< 4 | 2

A: Given curve, y=14x2-12lnx   ;  1≤x≤4

Q: Find the exact length of the curve. y = x2 - In(x), 1 < x < 4

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Q: Use the methods of this section to sketch the curvey =  x3  -3a2x +2a3, where is a positive…

A: The curve is  y =  x3  -3a2x +2a3, where is a positive constant.

Q: The horizontal asymptotes of the curve 12x y = (zª + 1)'/ are given by Y1 = and Y2 = where yı > Y2-

A: Asymptotes are the tangents where the function tends to meet at the extremities of the x and y axes

Q: Two different level curves of the graph of z = f(x, ygan intersect. O True False

A: The level curve of a function f of two variables are the curves with equations f(x ,y)= k, where k…

Q: The figure shows a semicircle with radius 1, horizontal diameter PQ, and tangent lines at P and Q.…

A: As per the question we are given a circle of radius 1 and a horizontal line above the x-axis. Now we…

Q: 4 The line y= -Lx+3 has a perpendicu lar which fangent to the graph of y= (x²-2) (2x+k) at x=-l,…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.