The function f : XI→ a + b cos x, is defined for 0 sxs 2n. Given that f(0) = 10 and that f (n) = 1 , find

Q: If f(x, y) = x cosy + ye*, find a2f дхду

A: Partial derivative: A partial derivative of a function is defined as the derivative of the function…

Q: Let F(u, v) be a function of two variables. Find a formula for f′(x) when             (a) f(x) =…

A: Given fx=F4x-4hence u=4x , v=4f'x=∂F∂u.∂u∂x+∂F∂v.∂v∂xBy chain rule      =∂F∂u.∂∂x4x+∂F∂u.∂∂x4…

Q: Find F as a function of x and evaluate it at x = 0, x = π/6, and x = π/2. X force 0 F(x) F(0) F(T)…

A:

Q: a) Differentiate the function Q(p) = -2³√/p³ (²-P). b) Hence or otherwise, determine Q'(1).

A:

Q: Find f. f"'(t)  = t   - √t

A: To find f"(t) we integrate f"'(t)

Q: Suppose the cost c of producing qa units of product A and qg units of product B is given by c=(3q°A…

A: Note:- We are entitled to solve only the first question, unless specified. Given:…

Q: Suppose that f′​(x)=2x for all x.   ​a) Find ​f(−4​) if ​f(0)=0. ​b) Find ​f(−4​) if f(2​)=1. ​c)…

A: Suppose that f'x=2x for all x. a To find f-4 if f0=0.b To find f-4 if f2=1.c To find f-4 if f-3=10.

Q: = f(x) = (4x – 2)(x² – 3). F %3D

A:

Q: 2. If f(x, y) = x² + xy − cos(xy), find the domain and range.

A:

Q: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

A:

Q: Find minimum of sin(x + 3) – sin(x + 1) – 2 cos(x + 2) where a E R.

A:

Q: The position of an object at time t is r(t) = (7 + t)i + e'j. Eliminate the parameter 1 to find y as…

A: Given the position of an object at time t is r ( t ) = ( 7 + t ) i + et j . We eliminate the…

Q: let f(x)= x2 . Find the value c in the interval (0,3) so that fave = f(c).

A:

Q: For the relation x²y - y² = 1 - x, find its first derivative at the point where x = 1 and y = 0.…

A: For the relation , to find its first derivative at the point where  .

Q: 49y" — 42y + 5y = 0, and - y(4) = 4, y'(4) = 1. y =

A: 49y''-42y'+5y=0, y(4)=4, y'(4)=1 Auxiliary equation 49m2-42m+5=0

Q: The function f(x)=tanx−x has a solution in the interval (1.5,3). If we perform False Position…

A: Given that f(x)=tan x-x in the interval (1.5,3) By regular falsi method,…

Q: (i) Find fæ, fy, fry, far and fyy for the function: f(x, y) = e¹y² + x³y³ . Verify that fry = fyx.…

A:

Q: Consider the following functions: (i) z = arctan (-) -(√) (ii) z= In (iii) z = (ex-ex) sin y. Which…

A:

Q: Let Find f(x)|x=7 = y = f(x) = ( 2 ) ²³ d dæ f(x)\x=7² sin x.

A:

Q: Let z be a function of x and y defined implicitly from the equation 9ye" - 5 cos(y+ z – 1) = 7x –…

A:

Q: Consider the function f(x) = cos(x2 - 2) + 1 on the interval (-3,3). Calculate the two x-intercepts…

A: f(x)=cos(x2-2)+10=cos(x2-2)+1cos(x2-2)=-1 As we already know, the solution to the trigonometric…

Q: Use the figures to evaluate the function if f(x) = sin x. (x,1) f(a + B)

A:

Q: The domain of the function f defined by is equal to: Select one: O True O False 7 cos(x)+y² In…

A: This question is based on logarithmic function.

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.