(b) A function f AR is continuous at a point c E A if for any e > 0, unere exists A one 8 >0 but de such that whenever 0 < x-cl < 8 and x E A it follows that f(x)-f(c)| ≤e+².

Q: (3-х, х <2 +1, x 2 2 B. Is the function h(x) continuous at x-2?

A:

Q: Suppose f is differentiable on the set of real numbers R and a E R. Let F(x)= f(xª) and G(x) =…

A: F(x)=f(xα)F'(x)=f'(xα)ddx(xα) , [chain…

Q: 3. Find the domain of the following functions: a.) f(x) = V1-x Inx b.) f(x) = Vx - 1lr

A: solutionsince the given (3)(c)f(x)=1-xlnx(b) f(x)=x-l ln(x)use have to find the domain of the…

Q: The function f(x) = 2 + 1/x is continuous on the following interval EXCEPT. O a. [-2,-1] O b. [1,2]…

A: At any point a for a function f(x) the limit limx→afx=L exists if the limx→a−fx=limx→a+fx=fa.

Q: 2. If function f(x) = 3²-12 is continuous at x=2, find f(x). x-2

A: We need to find f(x).

Q: Consider the function f (x) = 3 – |x – 4|| a. Graph the function and verify that f(1) = f(7) b. Note…

A: The given function is f(x)=3-x-4 The function can be redefined as  f(x)=x-1,      x&lt;47-x,…

Q: Suppose f and g are positive functions. Is the following true or false? Vf,g:N → R f(x) E O(g(x)) =…

A: Big-Θ notation: A function g(n) is in Θ(f(n)) if there exist constants c1, c2, and N such that…

Q: Determine b so that f(x) is continuous if O 8 x + 6 xS 6 f( x ) = D O 2 x2 + bx +10 x > 6 b =

A:

Q: For what value of a is x² -1, x< 3 f(x) 2ax, x2 3 continuous at every x?

A: Given function is Since, f(x) is continuous at every x, so f(x) is continuous at x=3.

Q: Let f : R → R, where f(n) = 5 . Answer the following questions. 7x²+3*

A:

Q: B. Determine whether f(x) (x - 3) (2x + 1) (x + 4) is continuous at x= 3.

A:

Q: - (т + 1)с, (2х + 1)с — г? — 5, if x 1 f(x) =

A: Given the function f(x).