Solutions Of Equations With One Variable

Question 1

What is the Intermediate Value Theorem?

Answer 1

For a continuous function f(x) on the interval [a, b] in which lies a real number L, there must be at least one ‘c’ such that c ∈ (a, b) , or a < c < b, and f(c) = L

Question 2

What is the root of a function/equation?

Answer 2

Let f(x) be a continuous function. If there exists a number ξ, such that f(ξ) = 0, then ξ is said to be the zero or root of the function f(x) = 0.

Question 3

What is a non-algebraic function?

Answer 3

A non-algebraic function is a function that includes trigonometry, logarithms, absolute value, and exponentials.

Question 4

What is the Bisection Method?

Answer 4

It is a way of determining the zero of a continuous function. This is done by bisecting the given interval, then selecting a subinterval with opposing signs at its ends. These steps are repeated until the root is found at the required precision level.

Question 5

What is the Intermediate Value Theorem?

Answer 5

For a function f(x) continuous over an interval [a, b] wherein lies a real number, L, there must exist at least one number ‘c’ which c ∈ (a, b) and f(c) = L