Q.2 Consider the function f(x) =- J1-x², 0

Q: c) Use Secant Method to find the root of f(x)= x -x-1 with two initial points x, = 1 and=1.5 and =…

A: Secant method Steps  Step-1: Find points x0 and x1 such that x0<x1 and f(x0)⋅f(x1)<0.…

Q: 4) Find the absolute maximum and absolute minimum values of f on the given interval. (a)f(x) = 3x² –…

A: Find the absolute maximum and absolute minimum values of fa) f(x)=3x2-12x+5 , 0,3 b) fx=x-lnx , 12,2…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. 8. f(x) = 2³3r² -…

A: In this question we have to find the absolute maximum and absolute minimum.

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 20 over the interval [1, 3].

A:

Q: Sketch a graph of the function f(x) 2 sin(2x). %3D -77/8-31/4-5n/8-/2 -3/8-7/4-T/8 t/4 3n/8- /25/8…

A: Given function is f(x)=-2sin(2x)We know that period of sin(x)=2πThe period of sin(2x) will be π and…

Q: 4. 1. Let f(x) = (sinx)*tan(1 – x)e30x. Find the maximum of f(x) in [0,1] and ɛ = 0.05. (by handly…

A: Given: fx=sinx6tan1-xe30x. We have to find the maximum of fx in 0,1.

Q: 1) Find the value of C that make the function continuous at x-1? x 1 -

A: We have given piecewise function  Function is continuous at x=1 if  f1+=f1=f1- f(x) = C-x        if…

Q: 2. Consider the functions f (x) 1 = - and g(x) = x² – 4 a) Let h(x) = (f ° g)(x). What is h(x)? b)…

A: Given query is to find the composite function and it's domain.

Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…

A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

Q: 1. Consider finding the root of f(x) =x´ – 5 use secant method, ɛ = 0, and start with the a interval…

A: given , f(x) =x2 - 5  we have to find roots of f(x) in interval by using secant method

Q: Q2/Show that the functions is harmonic u = 2 x (1 - y)

A:

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A:

Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

A:

Q: The function f(x)= (x² – 1)³, is decreasing on the interval (- 00 , – 2) U (0,2) ^O (-1,0)U (1, ∞o )…

A:

Q: 4 Given that f(2) is analytic at z = 0 and that f G) =, n = 1,2, 3..,find f(2). VE

A:

Q: 2. Find the linearization L(x) of f(x) = x³ - 2x + 3 at x = 2 and use it to approximate f(1.9) and…

A:

Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: +5, x <-1 Given f(x) = 3-x, -1< x s 1 x2+2, 1<x<2 X- Wx-2 + 4, x2 2 Find the point(s) where f(x) is…

A:

Q: 10. ( ) Find the absolute extrema of the funcion f(x) = 3 Vx2 - x on the interval -1, 1.

A:

Q: 1 - t Let F(x) = dt for -o << x < +∞ t2 + 24

A:

Q: 4. Determine the root of the given function using Secant method. Show the tabulated the results. Use…

A: The secant method uses the formula to perform the iterations and to approximate the root of the…

Q: A Function f(x) is defined for all xr>0, and satisfies f(x2) = x3 for all x > 0.Show that f is…

A:

Q: Consider the function f(z) = 2x+ 18z2-330z +37 defined on the interval -1, 10). Then the absolute…

A:

Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

A:

Q: 1 For a function f(x), we have f(x) = 1+ x? and f(0) = 0 prove that x +y f(x) +f(y) =f 1-xy

A: We will prove as following.

Q: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

A:

Q: 7) Find the absolute maximum of the function f on (0,E) S(x)= 10xe

A:

Q: 1. Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: see 2nd step

Q: 8. Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6].

A: Given : The function is f(x) = 6x + 4 +24x and the closed interval [ 1, 6 ].

Q: 12. Consider the function f(xx) = 2x² + y* + 4xy. %3D (a) Find the critical points for this…

A: Find the critical points of the function fx,y=2x2+y4+4xy

Q: 3. Find the location and values for any global extrema of the function 1 f(x) = ³ – 2x° +5 %3D on…

A:

Q: 1. Employ the following methods to find the maximum of f(x) = 4x – 1.8x² + 1.2x – 0.3x* (a)…

A: Given f(x)=4x-1.8x2+1.2x3-0.3x4. To find: (a) find the maximum using golden search method.…

Q: , 6]. che function on this interval. 1/sqrtx ow there exists a c in the open interval (2, 6) such tl

A:

Q: 3. Find the absolute maximum and the absolute minimum of f(x) = x-2 tanx on the interval [0,4].

A:

Q: 1. Let f(x) = 4x − 4x 2 . Verify that f(x) satisfies the conditions of Rolle’s Theorem on the…

A: Note:- According to the company policy we can attempt ?️ only one question so please upload the next…

Q: 2 4. Find the most general analytic function f(z) of the variable z = x+iy whose imaginary part is…

A: 4. Given vx, y=y-yx2+y2 as the imaginary part of the complex function f(z).   To Find: The most…

Q: 4. Show the function f(2)=21m(z) is differentiable or not differentiable at any points.

A:

Q: 2 The function f(x)= (x² – 1) ³ , is decreasing on the interval (- 00,-2)U (0,2) AO (-1,0) U (1, ∞ )…

A:

Q: 1. Consider the function f(x) = sinx - e-* has a root in the interval [0,1]. Use false position…

A:

Q: 9. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x³ – 2x2 – 5x + 6 on…

A: We have to find the value of c the solution is following

Q: Consider the function f(x) over the interval 0, 1. Does the extreme value theorem guarantee the…

A: Given function is f(x)=1sin πx4 over the interval 0, 1 and  q(x)=4x+32x2-1 Extreme value theorem: If…

Q: 7. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x* – 4x² on the…

A:

Q: Q2: Is the function f(x) = sin x -2x + x' odd or even Odd function C Even function C Not of all O

A:

Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

A:

Q: function, that is 0 everywhere except at t=0, is know as:

A:

Q: 3. Let f)=x+x+2x-1E2,lx). Then x= 1 is a root for r() of mmltiplicity 3D1 None 4 2

A:

Q: Q. 1: Determine the func- tion is continuous or dis- continuous at x = -1 and x = 1.

A:

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.