Construct an open cover for the interval [0, 1]. Verify that the open cover is in fact an open cover.

Q: The intersections with the abscissa axis of the image function are: f (x) = x2 + 10x + 21

A:

Q: Sketch the surface 1≤z≤ √9-x² - y² 1≤z≤√9-x² - y² and_x² + y² ≤1

A: Given is the surface surface 1≤z≤9-x2-y2 and x2+y2≤1 The objective is to sketch this surface.…

Q: 6. What does the n-th term test tell us about each of the following series? n n En=2 In(n) En=1…

A:

Q: where does this concave up and down?

A: A graph is concave up if f''x>0 and concave down if f''x<0. When f''x>0, it means…

Q: What does it mean for two families of curves to be mutually orthogonal?

A: Two families of curve are said to be mutually orthogonal if they intersect at right angles. Angles…

Q: Does this fuction have a minimum value?

A: The function Let

Q: Describe a way of showing that a continuous function on an open interval (a, b) has a minimum value.

A:

Q: Find the absolute Minimum value of y = 100 + 1800 on the closed interval [50 , 100]. Note : The…

A:

Q: State the open interval where the graph is concave up. f(x) = - 6x³ - 36x² + 6x A) (-6,∞) E) (-2∞)…

A:

Q: You are designing an RPG (role-playing game) for a gaming console and have decided to use an open…

A: Given that the function dx,y=e-x2y is to be minimised and maximised on the unit disc x2+y2≤900. We…

Q: What is the absolute maximum and minimum

A:

Q: Sketch the surface 1≤z≤√√9-x²-y²_and_x² + y² ≤

A: Solution is below

Q: 3. Show the limit x+y lim (x,y)-(-1,1) x+1+iny does not exist.

A:

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: