10:11 AM Mon Dec 527 of 86AAAAAA A A A A A A A A A A A A A A A A A A A A A A A A A11. Let f be the function defined by f(x)=√√x-2 for all x. Which of the following statements is true?(A) f is continuous but not differentiable at x = 2.(B) f is differentiable at x = 2.(C) f is not continuous at x = 2.(D) lim f(x) = 0x-2(E) x = 2 is a vertical asymptote of the graph of f.12. Using the substitution u = √x,(A) 25 e...apcentral.collegeboard.orgSi√√x(B) 2 e e" due" dudx is equal to which of the following?(C) 2₁²e". duDeel du(E)62%e" du

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Answered: ΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑΑ 11. Let…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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We have shown that the composition of two surjective functions is surjective, i.e. that if ƒ : A → B and g : B → C are surjective, then go f : A → C is surjective. Now decide whether the following statements are true or false, and prove your claim. Remember, to prove that a statement is wrong, all you need to do is to give a counterexample. (i) If f : A → B and g: B → C are functions such that go f is surjective, then f is surjective. (ii) If f : A → B and g : B → C are functions such that go f is surjective, then g is surjective. Get started by drawing some pictures of sets with arrows. No need to submit your drawings.
Let f be a real-valued continuous and differentiable function. Let function g be defined by g(x) = f(|x| + 2). A student presents the following proof to show that there exists a real number c € (-1, 1) such that g/(c) = 0. (1) Since f is a continuous function, so is g over the interval [-1, 1]. (II) Since f is differentiable, so is g over the interval (-1, 1). (III) It is evident from the definition of g that g(−1) = g(1). (IV) If the above conditions hold, then by Rolle's theorem, there exists dg(x) c = (-1, 1) such that gl (c) dx |x=c Which statement about this proof is correct? = 0. Step (1) does not hold, and hence Rolle's theorem does not apply. Step (II) does not hold, and hence Rolle's theorem does not apply. Step (III) does not hold, and hence Rolle's theorem does not apply. Step (IV) does not hold, and hence the conclusion is false. The proof is completely correct, and the conclusion holds.
Let f be a function defined on all of R that satisfies theadditive condition f(x + y) = f(x) + f(y) for all x, y ∈ R (a) Show that f(0) = 0 and that f(−x) = −f(x) for all x ∈ R. (b) Let k = f(1). Show that f(n) = kn for all n ∈ N, and then prove thatf(z) = kz for all z ∈ Z. Now, prove that f(r) = kr for any rationalnumber r.
Let us define a number a to be a fixed point of a function f if a = f(a). (For example, if f (x) = -x², then x = -1 is a fixed point because f(–1) = -1.) Prove that if f'(x) # 1 for all numbers x, then f has at most one fixed point.
Let f: X → Y be a function and A, BY be subsets of the codomain. a. Is f-¹(AUB) = f-¹(A) u f¹(B)? Always, sometimes, or never? Explain. b. Is f-¹(An B) = f¹(A) nf-¹(B)? Always, sometimes, or never? Explain.
10) The function f below satisfies Rolle's Theorem in the interval [a, b] because (a) f is continuous on [a, b] (b) f is differentiable on (a, b) (c) f(a) = f(b) = 0 (d) All three statement; A, B, and C (e) None of these
1. Consider the function fƒ: R → R defined by f(x) = = 2x + 1 5- 3x when x 1. A. Consider function f at the point x = 1. Is function f continuous at this point? Why or why not? B. Consider function f at a point x = C. Consider function f at a point x = a where a is less than 1. Is function f continuous at this point? Why or why not? a where a is greater than 1. Is function f continuous at this point? Why or why not?
Let f be the function defined by f (x) = = both increasing and concave up? O (4, ∞) (0,2) (2,4) O (-∞, 0) x²–2x+4 x-2 . Which interval is the graph of f
One and only one of the following functions is injective. Which one? Select one: a. f : R → R,ƒ(x) = \x + 31 O b.f : R → R,f(x) = 2×l O c.f : R → R,ƒ(x) = 3x² + 1 o R,f(x) = Vx² + 1 O e. f : R → R,f(x) = x³ – d. f : R → 1

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