Sketch f(x) = x^3-5.00x^2+1.01x+1.88, showing the roots near+-1 and 5. Write: x = g(x) = (5.00x^2-1.01x-1.88)                             (x^2) Find  the root starting from x0 = 5,4,1,-1. Explain the results. Find a form x = g(x) of f(x) = 0 in problem 1 that yields convergence to the root near x=1.

Q: at point x0=1 ,x1=1 and x2=2 f(x)=sin(x)+(x^2)+xe^2 function crossing second Write down the…

A:

Q: Find the local maximum of f(x) = -sin2x – x defined on 2'2

A:

Q: Find the derivatives of the functions in Exercis

A: Differentiation of the rational function can be done with the help of the differentiation formula…

Q: Find a rational (fraction) approximation for the value of 3√11 (square root 11, it wouldn't go…

A: We know that linear approximation (by using the tangent line to f(x) ) of f(x) at point (a,f(a)) is…

Q: ) The tangent line to y = f(x) at (-5, 2) passes through the point (-7, -5). Compute the following.…

A:

Q: Choose the correct answer by using the Product rule of derivative. d dx - (x4.x7) is equal to…

A:

Q: Find y' by in differentiation 1.) y= (x^2 + 1)^4 (x^3-10)^5 2.) y= 6x^2 (x+5)^3 / (2-x)^2

A: (1)      ddxx2+14x3-105 Apply the product rule: f·g'=f'·g+f·g' f=x2+14, g=x3-105…

Q: Form the polynomial equation with integral coefficients whose only roots are given. 2,-1,1

A: Given roots are 2,-1,1 Now we have to find the equation of polynomial with

Q: - Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

A:

Q: f(x) = (6x² - 2x+1)^

A:

Q: apply 1rt and second derivative to sketch graph  1)f(x)=3+7e^(-0.2x) and  2)f(x)=ln(2x+4)

A: In the question we have to draw the graph.

Q: 6. у3 2x – Jx² – 1

A: Given function y=12x-x2-1 we want to derivative of given function with respect to x

Q: Use the alternate definition, lim Ax)-Aa) to determine the instantaneous rate of X- a change of Ax)…

A:

Q: f(x)= (7x¹-5x-2)

A:

Q: Find the root between [-1,0] where \( f(x)=(x+2)^3+2x-5 \) with error \( \epsilon=0.1\) by using…

A: given equation is fx=x+23+2x-5interval -1,0find the root of an equation by using false position…

Q: FIND THE REAL ROOT OF X.EXP(X) = COSX BY SECANT ITERATIVE METHOD CORRECT UPTO 4 DECIMAL PLACES.

A:

Q: Example 3: Find the root of: f(x) = x' - 3x+1 in the interval [0,1]?

A:

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f(x) x - 1

A: To show the f(x) has roots between a and b we have to show that

Q: An object hangs from a string in a stable position and is represented by the function y = 4 sin (3x)…

A: NOTE:Use the form y= asin(bx−c)+d to find the variables used to find the amplitude, period, phase…

Q: 3) Use the Intermediate Value Theorur to show that there ís a root of the equation Make sure you…

A:

Q: Assume that f is a polynomial and x = 10 is a critical number for f If f''(10) = -sqrt2 what do we…

A: A function y = f(x) has a critical point at (x, y) if f'(x) = 0 or f"(x) is not defined. But as we…

Q: Find the equation of the tangent line to the graph of g(x) = f'(x) at x = -1 when f(x) = 5x³ + 2x² +…

A: Here, f(x)=5x3+2x2+2x

Q: Find local maximum or local minimum of f(x) = - sin 2x -x defined on 2'2

A:

Q: Find the derivative of the functron. Simplify and express the answer anly. using positive expenents…

A: In this question the given function is y=(x2-5)3x2+3 we have to find y' In positive exponents only

Q: Find the root between (2,3) of x3+ - 2x - 5 = 0, by using regular falsi method correct to three…

A:

Q: Find an equation of the tangent line to the graph of function f(x): 3 %3D x+5 at the point (2, ).…

A:

Q: Find the value of xg in 3 decimal places (positive root) using Secant Method (8th Iteration) f(x) =…

A:

Q: Find the root between [-1,0] where f (x) = (x+2)³ +2x – 5 with error epsilon=0.1 by using False…

A: The false position method is one of the methods used to find the approximate root of a function in a…

Q: Use the intermediate value theorem to show that there is a solution to x− √ x−ln x = 0 on the…

A: Use the intermediate value theorem to show that there is a solution to x− √ x−ln x = 0 on the…

Q: The 2nd approximation to the real root of the equation x³ – x² – 1 in the interval [1, 2] using…

A:

Q: 3 Show that f(x)= 1x-5 is NOT differentiable at 5 by using the defini tion of the derivative, (Start…

A:

Q: 4 3. Лх) — Зх - 5 %3D

A: Given that  f(x)=4/(3x-5)^2  To find the derivative of f(x)

Q: sinh 2x cosh 3xdx.

A:

Q: Find local maximum or local minimum of f (x)=sin 2x-x defined on 2 2

A: The given function is fx=sin 2x-x. Obtain the critical points as follows. Find f'x as…

Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

A:

Q: 3. Use the limit definition of a derivative to find f'(x) if f(x) = 3x2 - 5x %3D

A: f(x)=3x2-5x

Q: Find the specific that h (-3) =7 function satisfies hlx)こ 6-5x+x and

A:

Q: obtain a real root of a“ – 5x+1=0 with a = 0 until absolute error < 0.0001

A:

Q: 4) Use the Limit Definition of a derivative to find f '(3) if f(x): %3D 5-x

A: Given:- f(x) =2/(5-x)  To find:- Use limit Definition of a derivative to find f'(3)

Q: Give the result of every step in using the 4-Step Rule to find the derivative 14. f(x) = x3- 4x² + x…

A:

Q: 1. Find the derivative of f(x). 3x3 – 2x2- x- 5 | (a) f(x) =

A:

Q: Joha Find the derivative of the 1 1- f(x)= 2x+3

A:

Q: Find an equation of the tangent line to f at a = 9. (Express numbers in exact form. Use symbolic…

A: Topic:- limits and application of derivatives

Q: f(x) = (6x – 7)(2x + 3) %3D

A: Given  f(x)=(6x-7)(2x+3)

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f (x) = X - 1

A: Given that

Q: Find the smallest positive root for the given function by using the false position method with…

A:

Q: Find the derivative. Simplify completely. 1. f(x) = 4x³ cos x 2. g(x): Sx-4 In x 3. у sin x 4. f(x)…

A:

Q: Verify Mean Value Theorem for the function 3x² – 4x + 5 in [-1,1] 1-tanx

A: Use mean value theorem

Q: sech2(In x)

A:

Q: 4. Assume that æ € [0, 1] and write the error in the approximation to the error function using the…

A: