Problem 2: Determine whether the function f (x) = 3 - Vx+9 is continuous on the interval [0, 1.

Q: 4. Find two possible non-linear functions & and such that goh= √sinx-x²

A: To find the non linear function by the given composition.

Q: 3. Find the largest domain (in R2) for the function In(3 + y) 1- x + y f (x, y) :

A: Let's find.

Q: 7. If f(x)=√(1-1²)et² dt, on which interval is f decreasing?

A:

Q: √x² + y² x-1 (a) Find and sketch the domain of f (x, y). 2. Consider the function f (x, y) = 4 (b)…

A: The given function is  f(x,y)= x2 +y2-4x-1 We know that the domain of a function is the set of…

Q: Consider the functions f(x)= [x²-9 x*-1 2x ; x=-1 and (3x+2 g(x) = { x=-1 Define the new function…

A:

Q: Show that f(x) = x³ − x² − 3x + 1 has a zero over the interval [0, 1].

A: given function We need to sow that function has a zero on given interval.

Q: Does f(x) =x3 -1 on [-1,1] satisfy the conditions of Rolle's the Rolle's Theorem. Justify your…

A: Rolle’s Theorem: If a real valued function f(x) (i) is continuous on [a, b] (ii) is differentiable…

Q: 4. Show that the function f: R → R defined by f(x) = x² - 3x + 1 is not one-to-one.

A:

Q: 7. Determine each of the following for the function, f(x, y) = 7x³y² - 2x + 3y. Show all work toward…

A: Given,  f(x,y)=7x3y2-2x+3y

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.