The diagram shows the curve y= 4x –x and the straight line x=4.

Q: 2. Find the equation of the line that passes through the points of intersection of the curves y“ = x…

A: We plug x=y2 in…

Q: b. Find the slope of the curve at the given point. y* = 2x; (648,6)

A:

Q: c) Determine the nature of the turning points for the curve y = x5 – 5x4 + 5x3 – 1.

A: To determine the nature of turning points for the curve  y=f(x)=x5-5x4+5x3-1 we have to find out…

Q: Trace the curve: y^2 = (x-1) (2x+3) (3x-1)

A: First finding the zeros of  y2 =  (x-1) (2x+3) (3x-1) x-1 = 0 x = 1 2x + 3 = 0 x = -3/2 3x -1 = 0 x…

Q: c. The curve y= Inx, the lines x 4 and the x-axis.

A:

Q: Find the length of the curve. 1 10x3' y 6 + 1 ≤ x ≤4

A:

Q: 2. Trace the curve x3 – 6x² + 11x – y = 6. -

A: Given curve is, x3-6x2+11x-y=6 That is, y=x3-6x2+11x-6 1) Domain and Range of given curve:    This…

Q: Trace the curve x^3 − 6x^2 + 11x − y = 6.

A: Given- x3-6x2+11x-y=6 To draw- The graph of the above function. Concept used- The above expression…

Q: FIND THE PROPERTIES OF THE CURVE AND SKETCH FULLY x²-4x-12 6. Y = x²-2x-3

A: We have to sketch the curve Y2=x2-4x-12x2-2x-3 or Y=x2-4x-12x2-2x-3.

Q: nded by the curve y2=4x and the lines x = 1 and x = 4.

A:

Q: The distance of the line 7x+ y- 5=0 from the origin is A 2 B V2 D2/2

A:

Q: Find the slope of the curve y = 2x* + 3x + 2x? - 1 at a point where it crosses the x-axis

A: The point where y crosses x-axis the value for y is 0. Find the value for x for which y = 0.…

Q: Find the y-intercept of the line. y- 0.7x- 6.5 rintercept: 0

A: Line Y on X is  y=mx+c  m=slope and c=intercept

Q: Find the points of intersection of the curves y = 5x2 - 3x - 2 and y = 2x - 1.

A: We have the equation of curves as y=5x2-3x-2            ⋯⋯1y=2x-1                      ⋯⋯2

Q: Find the length of the curve Y 12x', 1<X< 2

A: Given curve is: Y=X55+112X3, 1≤X≤2 To find the length of the curve.

Q: Find the equation of the line tangent to the graph of y = 2x3 – 8x? + 3x – 6 at x = 1.

A:

Q: Find the slope of the curve x + y - 10y -3x +5 = 0 3-2x 2у-10 2x+3 10-2y 2x-3 10+2y 3+2x 2y+10 O…

A: We have to find slope

Q: The slope of the curve y = 5– 3x² at (-1, 2) is A. 5 С. 6 В. 2/3 D. -3

A:

Q: Write the equation of the line tangent to the graph of y? 2y + 10x 17 at (2, – 3). - The equation is…

A:

Q: Find the equation of a line perpendicular to y=−x−1 that contains the point (1,2).

A: We have to find the equation

Q: e of **y** where the two lines are equal? A y 4 -3 -2 -1 -2

A:

Q: Find the point inflection of the curve 2y=9x²-x³+6

A:

Q: At what point of the curve y = x3 + 3x are the values of y’ and y” equal?

A:

Q: Find the slope of the curve y =x + 2x^(-1) at point (2, 2). Select the correct response: 1/4 2 3/4…

A: We have to find slope of the given curve.

Q: find the slope of the curve x^2+y^2-6x-4y-21=0 at (0,7)

A: Given curve  x2+y2-6x-4y-21=0we find slope at (0,7)

Q: a. The curve y=4x-x and the lines y=0, x=1 and x=3.

A: Due to our guidelines we can answer only one question at a time, therefore I am answering first…

Q: Find the slope of the curve defined by the equation x²y – 8 = 0 at the point (2, 2)?

A: The required slope of the given curve can be found as below

Q: Determine the length of the curve x = (y-1), where 4 <y <9.

A: Now differentiating given curve with respect to y, we get

Q: Find an equation of the line L.L is perpendicular to y=3x.

A: y=3xWe compare it with y=mx+bSo, m=3

Q: Find the length of the curve y= 2²-√√x, 4 ≤ x ≤9. 23/2 3

A: To find the length of the given curve.

Q: Find the point on the line y = 5x + 4 that is closest to the origin. (х, у) %3

A:

Q: 3. At what point is 2 the slope of the curve y = 4x +x ?

A: Given,           Slope of the curve = 2    Curve y = 4x+x2         First we find y'        y'=  4+2x

Q: Find an equation of the line L. L is perpendicular to y = 2x.

A: In general, the equation of line is y=mx+c where, m=slope, c=y-intercept Given, y=2x  m=2

Q: The line shown above has an y-intercept of T

A: From the graph we can see that the line intersect the y-axis at y = 1

Q: Trace the curve: y^2 = 4x^2 / (x+5) (x-2)

A: We want to plot the graph ofy2=4x2(x+5)(x-2)=&gt;y=4x2(x+5)(x-2) The above expression exists…

Q: Perpendicular to the line y = 2x - 3; containing the point (1, –2)

A: Equation of a line passing through the point (a, b) and slope m is y-b=m(x-a)

Q: Graph the equations y = x2 and x2 + y2 - 7y + 8 = 0. At what point(s) do the curves intersect?

A: Graph the equations y = x2 and x2 + y2 - 7y + 8 = 0. At what point(s) do the curves intersect?

Q: a) when does the line x 2t, y = 3 +4t intersect the curve y = x2

A: Given data:     The given first line is: x=2t. The given second line is: y=3+4t. The equation of the…

Q: y = (x-5)(x+1)

A: Given equation of curve y=x3(x-5)(x+1)                   (1) We have to trace the curve of above…

Q: The point P(4, -2) lies on the curve y = -

A: As per our guidelines, we are supposed to answer one question at a time. Kindly repost other…

Q: B. Find the point on the line y = 10 – 2x that is closest to the origin. REFLECTION

A:

Q: Find the slope of the curve at the given point. y=2x^3−3x @ (-1,1)

A:

Q: Find an equation for the line perpendicular to y=-1/3x+6 with x intercept at x=4. Answer in y=mx+b…

A:

Q: Find the equation of the line that passes through the points of intersection of the curves y^2 = x…

A:

Q: Find the equation of the curve for which y"=6x^2, and which passes through the points (0,2) and…

A: The given differential equation is in the variable separable form and can be solved by integrating…

Q: Determine the nature of the turning points for the curve y = x5 – 5x* + 5x³3 – 1.

A: Turning point of a curve: Turning point is a point where the graph has the highest value (maximum)…

Q: Which of the following is the y-coordinate for the point that lies on the line y=-3/4x+1 and has an…

A: substitute the  value of x .

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.