Q3: Find f'(5) for f(x) = x³e-x, h= 0.01 using three points formula, compute the error

Q: Using the forward difference and values of h=0.1, to approximate the derivative of cos(x) at…

A: This is a problem of Numerical Analysis.

Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D

A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)

Q: 3.Using simple fixed-point iteration, determine the root of the equation f(x)= sin (Vx)–. X, = 0.5…

A:

Q: Use Secant Method to approximate the root of the function: f(x)= x2 - 5 at Xo = 2, x1 = 3 What is…

A: we have given the function f(x)=x2-5     x0=2, x1=3 we have to find the approximated root after the…

Q: The derivative with respect to X .2 y = x sin-'x + V1 – x²

A: Given:               y=x sin-1x+1-x2 Differentiate with respect to x           ddxy=ddxx sin-1x+1-x2…

Q: 2. Find the root of the function using Fixed-point Iteration. f (x) = x cos (x) - x?

A: Consider the given function as, fx=xcosx-x2

Q: Q1. Use Newton-Raphson method to locate the first positive root of f(x) = tanx - 2tanhx = 0

A: In Newton-Raphson method  x0 is the initial solution of f(x) then further solutions are obtained…

Q: 3. Find the derivative of g(z) = V9- using the definition of derivative.

A:

Q: 5/ Use the Newton - Raphson method to estimate the root of f(x) = e - x, employing an initial guess…

A:

Q: Find a root of the equation 3x + sin(x) - e* = 0 using Newton Raphson Method. Consider initial guess…

A: Let fx=3x+sinx-ex Then f'x= 3+cosx-ex Given that x0=2·500

Q: Find the root of the function using Fixed-point Iteration. f (x) - x cos (x) - x?

A:

Q: Find a root of an equation f(x)=x3-x-1 using Newton Raphson method.

A: We will find out the required root.

Q: Find the approximate error, relative approximate error, and absolute relative approximate error of…

A: The approximate error is calculated using the formula: Ea=Present value-Previous value. The relative…

Q: Solve using linearization using one digit approximation only 1) f(x) = V5

A:

Q: Use Newton's Method with the function f(x) = x² – 2 and initial value xo = 3 to calculate æ1, x2,…

A: Newton's approximation method is used .  x1,x2,x3 are calculated or n =0,1,2 respectively.

Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: b) write an expression for the position in terms of time t, use c (lower case) to denote constant of…

A: a =dv/dt where a is acceleration

Q: 2) Find the first derivative: a) y = cot * (3x² +7)

A: Differentiate wrt x

Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

A:

Q: cosh r – 1 · (xª4 + 2) +2). Compute the derivative of y = In | (2x + 1)

A: Given problem:-

Q: 5) Find the second derivative of f (x) = %3D ex plify your answer as much as possible

A: fx=1-2xexTo find the second derivative

Q: 6) When estimating the roots of the function f (x) = (x + 3)3 (x – 1) using Newton Method, find the…

A: The asymptotic error constant is given by the formula . Here, x' is the actual root of the function.…

Q: Approximate the length of the curve using n secant lines for n = 2; n = 4.y=ln x, 1>=x>=3

A: We have been given a curve y=lnx and we are supposed to approximate the length of this curve between…

Q: Find the relative extrema of f(x) = 8+72x – 9x? using both first and second derivative tests. f (x)…

A:

Q: Find a root of an equation f(x) = cos(x) - − using Newton Raphson method

A: Let us start solving the problem step by step  Given  Cos(x)-(x/6)=0 Let f(x)= cos(x)-(x/6) We will…

Q: Q8/ Use implicit differentiation to find of the following curve at the point (2, 3). dx2 2x3 – 3y2 =…

A:

Q: 1 at x= 4 by using the 2Vx Q2. Find the slope of the tangent line to the function f(x)= definition…

A:

Q: Use Newton’s method to approximate an intersection point between f(x) = tan(x) and g(x) = 2x. Use…

A:

Q: B. By using the definition of the derivative, find the for: dx 1- f(x) = V %3D 2- f(x) = x -!

A:

Q: Use forward-difference formula to evaluate the first derivative of y = tan(r) at a = using a value…

A: We know that the forward difference formula is: f'(x)=f(x+h)-f(x)hThe given function is : y=tan(x)We…

Q: Q:1 Find the second derivative of f(x) = 2x5 - 3VX7 at x = 1 rounded to five decimal places.

A: To find the second derivative of  f(x)=2x⁵-3x7/3 at x=1

Q: Use Newton's Method with the function f(x) = x² – 2 and initial value xo = 1 to calculatex1,X2, X3 .…

A:

Q: Q2// Use Euler's method (with all details) to find approximate value of y when x = 3 of = 2y-2x²-3,…

A: The Given initial value problem is: dydx=2y-2x2-3, y(0)=2, h=0.3 To find: y(3) using Euler's…

Q: To begin with, calculate the first derivative f'(x) = Now use this derivative to find the critical…

A:

Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

A:

Q: Use Newton's Method with the function f(x) = x³ – 5 and initial value xo = 1.5 to calculate æ1, x2,…

A:

Q: Q2: What is the value of second derivative of f(x)=3 sin((1-x)/t) *

A:

Q: 4 %3D ») f(E) =

A:

Q: Find the derivative. 8 + e y = In 8 + et 8 - ex.

A: Given,          y=ln8+ex8-ex

Q: using the forward divided difference approximation with a step of 0.5, what is the derivative of…

A:

Q: How do I find the 20th derivative of f(x)=(2cos x)(cos 3x)? I think there must be some trick because…

A: Given:

Q: Find a root of an equation f(x) = x^4-2 using Halley's method.

A:

Q: Q10) use the Chain Rule to find the derivative of w- xy With respect to t along the path x-cost,…

A: w=xy  x=cos t , y=sin t

Q: the root of the function f(x)= (x power 3) +x -1 obtained after first iteration on application of…

A:

Q: c. Find the derivative of y =+- et x3 cOS X 2

A:

Q: Find the first derivative or f(x) of the following functions using the techniques of integration.

A:

Q: Using the three-point midpoint formula, find the approximate value of the fist derivative of f(x) =…

A: To approximate the value of the first derivative of the below function at x=2 with h=0.1. fx=xex

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.