Which of the following functions are integrable. a b C d f(x)= in [-1,1] f(x)=x²+1 Both b and d f(x)= in [-4,0] [x+1 when x<1 (2x+1 when x21 in [0,3]

Q: Let f(x) be a function which is twice differentiable with f"(x) > 0 on the interval [a - 1, a + 1]…

A: Given that f(x) is a function which is twice differentiable with f"(x)&gt;0 on the interval…

Q: Define f(x) = x if x is rational and f(x) = 0 if x is irrational. Compute So f dx and ſ f dx. Is f…

A:

Q: Least residue of 8^68 modulo 17

A:

Q: (a) Apply first principles, to calculate the differential coefficient of (x) = 5(3x²+2) when x = 3.

A: Solution a: Given function is f(x)=5(3x2+2) using first principle…

Q: 6. Let f be continuous on [a, b]. Show ffdF = f(x) [F(b) – F(a)] for some x € [a, b].

A: This is a consequence of the intermediate value theorem

Q: True or false: If f: (0, 1)→ R is defined by f(x)=√x for every real number a in the open interval…

A: fx=x for all real xin the open interval  0,1

Q: Let 4 – x² if x > 1 f(r) if x < 1 Determine whether or not f (x) is continuous at r = 1.

A: If left hand limit and right hand limit same, then f(x) is continuous at x=1.

Q: Let A = R {3}, B = R - {1}, and let 1 x-2 Isfinvertible? Explain. x-3 f: A B be defined by f(x)=

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Suppose that f is a continuous function on the interval [0,3] such that f(0) 4. Apply the…

A:

Q: 1 If the function f is continuous on [a,b], then there exists at least one number C in [a,b] such…

A: If the function f is continuous on [a, b], then there exists at least one number C in [a, b] such…

Q: Vhich of the following functions is continuous on the interval (- 0, + ∞ )? @ f(x) =Vx²-1 B…

A:

Q: 7. By Principle of Mathematical Induction prove 5º – 1 is divisible by 2 for all n>1

A:

Q: The iteration of the Bisection method can be stop when f'(c.) - 0. False True The Newton-Raphson…

A: As per guidelines, I can answer only three subparts.

Q: Prove f(x) = x2+4 is not uniformly continuous on R.

A:

Q: Consider the function f: RR defined by f(x) = 0 if x is irrational and f(x) = 1 if x is rational Is…

A: Note: f is said to be Riemann integrable on [a, b] if To Prove Dirichlet's function which is defined…

Q: Suppose that f is a function which is integrable on the entire real line, and that a and b are real…

A:

Q: t 0, if x is irrational 1, if x is rational ve a rigorous proof that f is not integrable on the…

A:

Q: Let f(x)=1/x. Show that f is bounded from above on any interval (α,1), where α>0, but the function…

A:

Q: Consider the function g: RR defined by g(x) = 0 if x is irrational and g(x) = 1/q if x = p/q is…

A: To show that a function is riemann integrable we have to show that for any e&gt;0,…

Q: Which of the following functions is continuous on the interval (-0, +)? …* f(x) = Vx² – 1 (A f(x) =…

A: