continuous on [a,b] and for a given & > 0 there exists a - P(x)|

Q: If f(x) = g(x) for x # c and f(c) # g(c) then either f or g is not continuous at c.

A: Continuous Function:In mathematics, a continuous function means that a continuous change in the…

Q: f(x) = x² - 2, x + 4, O true false x 3 is continuous everywhere.

A: f(x) = ( x2-2, x<=3            x+4, x>3

Q: Show that f is continuous on (∞ , -∞ )  .

A: we have to show that f(X) is continuous in (-∞,∞). f(x)=x2             if   x<1           x…

Q: Consider the function f defined by f(x) = x lxl for each * € R. How many times is f differentiable…

A: To determine the differentiability of the function  on  and , we need to analyze the derivative of…

Q: 6) Determine constants a and b such that f(x) is continuous for all values of x. ax + 3, if x> 5 8,…

A:

Q: Where is f(x)= -5 -6z+5 discontinuous?

A: The given function is fx=x-5x2+6x-5. We have to find the point where the given function is…

Q: n a and b with f(c) = N. I thi

A: Mean value theorem: Rolles theorem If a real-valued function f is continuous on a proper  [a, b],…

Q: If that f is continuous on a sxsb. Let F(x) be any of f(x). Then, f(x)dx = F(b) - F(a). This theorem…

A: Recall: Mean value theorem: If f(x) is continuous over an interval [a,b], then there is atleast one…

Q: If f is a continuous function on [a, b], ƒ is differentiable on (a, b), and if both f(a) and f(b)…

A: This question is based on Rolle's theorem which is explained in step 2.

Q: Suppose that a < b <c and f is continuous. Select all true statements. (a) f(x) dx = f(x) dx – f(x)…

A:

Q: Show that if f"(x) < 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] < favg < f[(a+b)/2]

A: Consider the given information. f"(x) &lt; 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] &lt; favg &lt;…

Q: A function is said to be Hoelder a continuous on [a, b] iff |f(x) – f(x')| 0. Show that if a > 1…

A:

Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…

Q: Let n > 2 be a natural number. Prove that there is no continuous function q : C → C such that…

A: