Find the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at each point is 3√x.

Q: Find the exact length of the curve.   y= 2/3x3⁄2,    0 ≤ x ≤ 4

A: Given query is to find the length of the curve for the interval.

Q: Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x %3D

A: Given , the function f(x) = x2 - 2x Now we find      f(1) = 12 - 2•1 = 1 - 2 = -1,…

Q: Determine equations of all lines tangent to the graph of f(t) = t° /3+2t² +4t that have slopes of 1.

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Q: Find a function f (x, y) that has the line y = 3x - 4 as a level curve.

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: Find the equation in the xy-plane whose graph includes x In(6t) and y = t².

A: Given  x= ln(6t) y=t2

Q: Q5: (A): Finding a curve whose slope at the point (x, y)is 3x² if the curve is required to pass…

A: if the curve is passing through the point (1,-1) then we have to find the curve if the slope of the…

Q: Find the x- coordinate of the inflection point(s) of the | .2* curve y = -7xr'+ 4x +10.

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Q: Find the points on the curve x^2y = 2 nearest the origin.

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Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

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

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Q: Find the slope of the secant line connecting the points on the graph f(x)=2h+4x-12, with the given…

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Q: Find the exact length of the curve. y = 4 + 6x3/2, 0 < x < 1

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Q: Find the coordinate of the extrema of the curve y = x² – 4x + 1.

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Q: Find the exact length of the curve. y = 5 + 2x³/2, 0< x < 1

A: Given: y=fx=5+2x32, 0≤x≤1 we know that lengthL of curve in interval a,b is given by L=∫ab1+f'x2dx…

Q: Find the exact length of the curve.   y2 = 4(x + 4)3 , 0 ≤ x≤ 2 , y&gt; 0

A: Given: y2=4x+43,0≤x≤2,y&gt;0 To Find: Find the Exact length of the curve. Concept: Length of the…

Q: Find the length of the curve: x3 1 y = - 3 4x' 1<x< 3

A:

Q: find the length of the remaining part of the y = x³/12 + 1/x curve between the x = l and x = 2 apfog…

A: We have to find the length of the remaining part of the curve y=x312+1x between x=1 and x=2

Q: The slope of the curve y =x' + 3x² – 4x+5 at (1,5) is O a. 0 O b. 2 O c. 5 O d. 4

A:

Q: Find the equation of line (L) that passes through the intersection point of the two functions y = v2…

A: In this question given that two line which are intersect each other and and a line is perpendicular…

Q: Q1/a) Find the curve whose slope at the point (x,y) is 3x2 if the curve is also passes through the…

A:

Q: Find the length of the curve y= 3/2x^2/3 from x = 1 to x = 8

A: Given,         The length of the curve y=32x23 from x=1 to x=8.We know that,         The length of…

Q: Find the exact length of the curve. y = 3 2x3/2, 0 < x < 6

A: We have to find length of curve

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: Find the exact length of the curve.   y = 1+ 6x3/2 , 0 ≤ x ≤ 1

A: Find the exact length of the curve.

Q: Determine the point(s) at which ƒ(x) = x3 - 12x has a horizontaltangent line

A: The points where the tangents are horizontal are the points at which slope is zero.That means,…

Q: Find the length of the curve. y= (16-x2/3)3/2 from x=1 to x=64

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Q: Find the exact lenght of the curve. when 0 is less x and x is less than or equal to 1 y=2+2x3/2

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Q: Find the exact length of the curve. y = 5 + 2x³/2, 0≤x≤ 1 2.268 X

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Q: Find the length of one branch of the curve ay? = x3 from x = 0 and x = 5a. 4.

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Q: For what value of x will the curve y = x3 - 3x2 + 4 be concave upward?

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Q: Find the slope of the curve at the indicated point. y = x2 + 3x - 5, x = 2 O m = 7 O m = 2 m = 10…

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Q: Find the exact length of the curve. x3 y = 1 + 4x 1< x < 3 3.

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Q: find the equation of the secant lines of y=√x passing through the points: x1=1 and x2=2

A: Secant line for a function between two points on a curve is simply a straight line passing through…

Q: Find the exact length of the curve. x3 y = 1 < x < 2 %3D 4x

A: y=x33+14x  ,  1≤x≤2.

Q: Find the point on the graph y=Vx+1 that is closest to the point (2, 1).

A:

Q: The equation of the curve in the tx-plane which passes through the point (2,3), and has, at every…

A: In this question, slope of curve and point is given and we have to find out equation of cuve.

Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A: We have to find the value of a and b according to the given information

Q: / Find the length of the curve y = (÷) (x²

A: Given,         y=13x2+232

Q: Compute the length of the curve: f (x) = x² 2x, 0<x<2

A: Given:- f(x) =x2 -2x  To find:-  Length of curve over interval [0, 2]

Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

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Q: (b) Show that the points of inflexion of the curve y = (x- a) (x – b) lie on the | line 3x +a =4b.

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Q: How far from the x-axis is the center of the curve 2x2 – 2y2 + 10x – 6y – 55 = 0?

A: The given equation of the curve is: 2x2 – 2y2 + 10x – 6y – 55 = 0 This can be written as:

Q: Find the angles at which the curve y=x3−x intersects the x-axis.

A: The angle at which curve intersect the x axis is determined by the angle of slope of tangent to the…

Q: Find the y-intercept of the line tangent to y=(x' – 4x² + 8)en * at x = 2. а. -21.032 b. -2.081 с. 0…

A: Topic:- Application of Derivative  Correct option = d

Q: Find the length of the curve y = x^4 for 0&lt;_x &lt;_1

A:

Q: (b) Use the result of part (a) to find the direction in which the function f(x, y) = x³y - x²y4…

A: Given:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A:

Q: Find the points on the curve x2y = 2 nearest the origin.

A: The curve is x2y=2 Let x1,y1 and x2,y2 be two points, distance betwwen these points is x2-x12+y2-y12

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.