Q.1. Apply three steps of steepest descent to f (x) %3D 2(х,2 + х?2) +x;x, — 5(х, + х2) with initial point x0 3D [1 -2]T

Q: 1. If g(x) = 3x - 7, find i. g-¹(x), ii. g-¹(8) 5 x+8' 2. If h(x) = i. find h-¹(x), ii. h-¹(3)

A: Given : g(x)=3x-7 and h(x)=5/(x+8)  We have to find inverse of these functions.

Q: Find S° g)(x) and write the domain in interval notation. e) - V2 -x 16

A: f(x) = 3/(x2-16) and g(x) = √(2-x)

Q: Find the interval(s) where f(x) = 2x° – 15x? + 36x – 27 is increasing. -

A: The given function is fx=2x3-15x2+36x-27. The main objective is to find the intervals where the…

Q: Use the given graph of y = f(x) to solve for what value(s) of x is f(x) = 1?

A:

Q: of of For the function f(x,y)% 9x2- 3y°-4, find and dx dy of II

A: While calculating the partial differentiation of a function with respect to X we consider the other…

Q: (5) Given z=x³y-3y². If x changes from 2 to 1.9 while y changes from 1 to 1.02, find dz and Az. Is…

A: The objective of this question is to find the change in z (dz) and the approximate change in z (Δz)…

Q: For y = f(x)=x² - 2x +9, find dy and Ay, given x = 1 and Ax = -0.1.

A: Given,            y=f(x)=x2-2x+9. and  x=1, ∆x=-0.1. To find dy and ∆y.

Q: Find the general solution of the given bessles differential equation at (0, 0) d²y dy 1 = 0 625. +x-…

A:

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: Find the absolute extrema (max and min) of the function f(x) = ex 2−4 on [ -1,2]

A:

Q: Determine all inflection points. 3 f(x) = 4x° - 12 , xER

A: Find all inflection points  fx =4x3-12 inflection point is point where f''(x) is equal to zero or…

Q: 1 Q 2. Differentiate h(x) = (V+ -2 IX

A: The equation can be re written as,

Q: 02.Find all the maxima value of f(x, y) = 49 – x2 - y?, on the line x +3y = 10 %3D

A:

Q: Given the equation 3y - 9x + 6 = 0, find f'(x) %3D using slope-intercept form.

A:

Q: 1. Find the intercepts of the function. f(x)-x* +2 а.

A: Given data÷

Q: (2 Ost<3 If f(t) = - -2 t23 then f(t) in terms of unit step function equals Select one: a. -2+2uz(t)…

A: You just need the definition of the unit step function.

Q: Use the method of separation of variables to solve : xyu̟ +2u, = 0, Q.4 U(x,0) = 3x*.

A:

Q: Linear Function: g0) = 4x-2 a. What is the domain of f0) and g(x) ? b. What is the înitial value of…

A: Given function is g(x)=4x-2

Q: Find the roots of the function f(r) = (2" – 1) - (7 +2r – 3) with z ER. %3D

A:

Q: For the function f(x,y) = 3 x³ + 5y4 5 4 x +y find f, fy, f(-1,1), and f,(-3,2).

A:

Q: y = sin(2x – 27)+1

A: