B) Find the approximate roots of the following equation: f (x) = x³ – 8 = 0, on the closed interval [0,3]. %3D

Q: The ABC toilet manufacturing company is planning on improving their float devices by determining its…

A: The function given is as follows: fx=e-2x+1-2x+1 We are asked to find the root of the above function…

Q: find the seril solution of the equation y``+  4xy = 0  at the neighborhood of the  point  x0 = 0

A:

Q: Determine the value of y in the given equation in the interval [0, 2rT): 2cos-y - 3cos y = -1

A:

Q: If f(r) = 4x? 3x +5, find f'(- 2). Use this to find the equation of the tangent line to the parabola…

A:

Q: Without solving, match a solution curve of  y'' + y = f(x)  shown in the figure with one of the…

A:

Q: ind the equation of the line tangent to the curve 3x² + 16y² = 192 at the point Mx + K. P= (-4, 3)…

A:

Q: For f(x)=x3+3x2 -9x+4  Find the values of x where the tangent line is horizontal and the equation…

A: Tangent is horizontal line when it's slope is zero.

Q: apply 4th order Runge-Kutta to solve the following value problem y = x^2 + y for h = 0.1, y(1)=1 and…

A: The given function is fx,y=x2+y And x0=1,y0=0.1 since the step size h is given as h=0.1. Now to find…

Q: a. Determine the point (a, la)) for which f'(a) = a, given that Ax) = -x + 3x-7. b. Write the…

A: For (a), Given: We need to find the point a for which f'(a)=a. Here, f'(x)=-2x+3. So,…

Q: By using fixed points find the roots of equation f(x) = x + 4x –- 2 x, = 0 E= 0. .0001

A:

Q: A. Solve the following DE by using exact equation method: y = x- y,

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: Q.4 (A) By using NRM, find the real root of x3 – 2x – 5 = 0 accurate to six decimal places in the…

A: (A) Given: x3-2x-5=0 Differentiate the function with respect to x. ddxf(x)=ddxx3-2x-5f'(x)=3x2-2…

Q: For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show…

A:

Q: A. Solve the following DE by using exact equation method: y = x - y,

A: The given differential equation is dydx=x-y ⇒x-ydx-dy=0 ⇒M=x-y and N=-1⇒∂M∂y=-1 and ∂N∂x=0⇒∂M∂y≠∂N∂x…

Q: If f(x) = 4x? 6x + 7, find f'(– 2). - Use this to find the equation of the tangent line to the…

A: AnswerGiven f(x)=4x2-6x+7f'(x)=ddx(f(x))wktddx(xn)=nxn-1f'(x)=ddx(4x2-6x+7)f'(x)=8x-6at…

Q: B) Find the approximate roots of the following equation: f(x) = x3 – 8 = 0, on the closed interval…

A: Roots of an equation f(x): roots of an equation are those values of x for which the function f(x) =0…

Q: Q6. Use the method of Variation of parameters to solve (i) y" +y : tan x.

A:

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: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

Q: Given x(t) as shown

A: Given, x(t) as shown :

Q: Q4) B: Solve for x: (*+V+y sin2x)| - <4ta laxdy

A: Solve for x: ∂2∂x∂yy3+x−4+ysin2x&lt;4cos2π

Q: Find two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the…

A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…

Q: If f(x) = 5x2 - 4x, find f'(2) and use it to find an equation of the tangent line to the parabola y…

A: Given that fx=5x2-4xTo find : equation of tangent at point 2,12 and f'2Solution…

Q: 1. (a) Solve for the general solution y' + (cotx)y : = xCScx

A: Solution1;a Given the diffrential equation yι+cotxy=xCScxGiven the diffrential equation  is of the…

Q: Estimate solutions of the following equation using a Graphical Estimation method. (You need to show…

A:

Q: if f(x)=6x^2 - 4x, find f'(2) and use it to find the equation of the tangent line to the parabola…

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: (D² + 1)y = sec² x csc x X cSC X

A:

Q: The formula for solving for the area in the first quadrant bounded by y = x², the circle x² + y² =…

A:

Q: Use an appropriate substitution to solve the equation z15 and find the solution that satisfies y(1)…

A:

Q: Find an equation of the tangent line to the curve

A:

Q: If f(x) = 4x? – 2x + 4, find f'(1). 4x2 – 2x + 4 at the point (1, 6). The Use this to find the…

A:

Q: If f(x) = 2x2 – 2x + 4, find f'(– 4). 2x + 4 at the point (– 4, 44). Use this to find the equation…

A:

Q: 1. Find the equation of a curve that passes through the origin and satisfies (1 + x²)y' + 2xy = 4x²

A: Given differential equation is  1+x2dydx+2xy=4x2 Simplify the given differential equation we get…

Q: Determine the r values for which the f unction y(x) is solution of the x² + 1 equation y – 2xy? = 0

A: We have to find

Q: Of the solutions to the three di↵erential equations above which one is increasing at (1, 1)? Explain…

A:

Q: Solve for at least one possible root for the function x3 + 2x + 2 = 10e-2x² using the methods…

A: Note:- Fixed point iteration method is also called Method of Successive Substitution (MOSS). Fixed…

Q: 3 | co - 4. Find the length of the curve y = 7(6+ x)2 from x = 189 to x = 875.

A:

Q: Q5: Does any tangent to the curve y = vx cross the x-axis at x=-1 If so, find an equation for the…

A: To find: The equation of tangent to the curve y=x if possible. Given: The equation of the curve y=x.…

Q: 1. Find the equation of a curve that passes through the origin and satisfies (1+x²)y' + 2xy 4x2

A: To find the equation of the curve

Q: Find the maximum of the following equation f(x) = -4 x³ +3 x² + 25x + 6 By using newton's method,…

A:

Q: solve the following non-linear equation with secant method xex - cosx = 0

A:

Q: Q2: Find General Solution (YGS)to the equation (Yª-1) Y=COS(2x)

A: From the given information. The given differential equation is as follows.

Q: Find an equation of a line tangent to the graph of h(x) =s at x-2 y=6x+13 O у-бx+13 y=6x+12 O…

A:

Q: Q6. Use the method of Variation of parameters to solve (i) y" + y = tan x.

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

Q: Q4) f(x, y) = x'/3 – x/ay² is harmonic ? Does the function

A: our objective is to conclude result.

Q: ty" – (t+ 1)y' + y = t?

A:

Q: Find an equation for the e Foci: F(±2, 0), ver

A: The focii of the ellipse is ±2,0 . The vertices of the ellipse is ±3,0. The equation of the ellipse…

Q: Q2)B/ Find the points on the curves y(X) given by y = x - 6x? + x+3 where the tangents are parallel…

A:

Q: (D² + 1)y = sec? x csc x

A:

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.