Homework Answers
Options b,d,e,f are True .
Option a is false , you can take f(x)=|x| as a counter example.
Option c is again false because it behaves like mod function at x=4, that is it has a sharp edge at x=4.
Options d and e are true because we have compact domain.
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Question 2 Please
(2) (6 points) Indicate (by circling the letter) which of the following statements...
Write ‘T' for true or ‘F' for false. You do not need to show any work...
Write ‘T' for true or ‘F' for false. You do not need to show any work or justify your answers for this question. The questions are 2 points each. (a) __If (xn) is a convergent sequence (converging to a finite limit) and f:RR is a continuous function, then (f (xn)) is a convergent sequence. (b) _If (xn) is a Cauchy sequence with Yn € (0,1) and f :(0,1) + R is contin- uous, then (f(xn)) is also a Cauchy sequence....
QUESTION 1 (A). Stationary points For the notion of a "stationary point" to make sense for a function f: R&#...
QUESTION 1 (A). Stationary points For the notion of a "stationary point" to make sense for a function f: R" R the f function J must be at least: Select one: a. Infinitely differentiable b. Not everywhere zero C. Continuous d. Once differentiable e. None of the other options listed (B). Lagrange multipliers A (single) Lagrange multiplier arises from the requirement that Select one: a. a cross product is nonzero b. two numbers are proportional C. two square matrices are...
With justification in each one. Clarification; why if true and why if false? Please Determine whether...
With justification in each one. Clarification; why if true and why if false? Please Determine whether the following statement is true or false: • Iff: R+R is differentiable and strictly increasing on R, then f'(1) > 0 VI ER • If S: R R is continuous and f(x) - ron Q, then (V3) - 3. • If f,g: (0,1) - Rare functions such that \S(1)-f(y) = g(1)-9(y) for all 1, y € (0, 1) and g is continuous on (0,1),...
(1 point) Enter a Tor an F in each answer space below to indicate whether the...
(1 point) Enter a Tor an F in each answer space below to indicate whether the corresponding statement is true or false. A good technique is to think of several examples especially examples which might show that the statement is false! You must get all of the answers correct to receive credit. 1. Every differentiable function on the interval (4,5) must have both a maximum and a minimum 2. Every differentiable function on the interval (-3,0) must have a minimum....
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then...
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...
Please indicate whether the following statements are true or false by circling a T or an...
Please indicate whether the following statements are true or false by circling a T or an F (true or false) 1. Direct and indirect materials may both come from the same source [ ] [ ] 2. Factory overhead includes the cost of selling and advertising the product [ ] [ ] 3. Fixed costs remain constant in total, the average fixed costs becomes progressively smaller as the level of activity increases [ ] [ ] 4....
True or False Evaluate each of the statements below as true or false.
True or False Evaluate each of the statements below as true or false. a) A critical number of a function f(x) can only be defined as a number c in the domain of f(x) where f'(c) = 0). b) If f(x) is a continuous function on [a,b], then an absolute maximum ſ(c) and an absolute minimum f(d) for some c, d in [a, b] are guaranteed to exist. c) If f'(c) = 0, then f has a local maximum or a local minimum at...
Question 6 (1 point) Suppose a function f(x) is differentiable everywhere and has a local minimum...
Question 6 (1 point) Suppose a function f(x) is differentiable everywhere and has a local minimum at x=c. If f(x)<O when x<c, and f'(x)>0 when x>c, then by the Global Interval Method we know x=c is O a local maximum an absolute maximum a local minimum an absolute minimum
10. (18 points total: 3 points for each correct answer, 0 points for incorrect answers or...
10. (18 points total: 3 points for each correct answer, 0 points for incorrect answers or no answer Answer "True" or "False” for each of the following: (i) If 8,9:R + R and are both continuous at a number c, then the composition function fog is continuous at c. (ii) If functions hi, h2: R + R and are both uniformly continuous on a non-empty set of real numbers E, then the product h h2 is uniformly continuous on E....
2. Indicate which species are aromatic by circling them. [4 points] 3. Predict the product(s) obtained...
2. Indicate which species are aromatic by circling them. [4 points] 3. Predict the product(s) obtained in the following electrophilic aromatic substitution reactions. 12 points each] o HNO3 њео, F: d) Br2 Fsc FeBr3 a) Cl H2N e) H2S04 b) AICl3 H3CO c) Cl AICl3
Write ‘T' for true or ‘F' for false. You do not need to show any work or justify your answers for this question. The questions are 2 points each. (a) __If (xn) is a convergent sequence (converging to a finite limit) and f:RR is a continuous function, then (f (xn)) is a convergent sequence. (b) _If (xn) is a Cauchy sequence with Yn € (0,1) and f :(0,1) + R is contin- uous, then (f(xn)) is also a Cauchy sequence....
QUESTION 1 (A). Stationary points For the notion of a "stationary point" to make sense for a function f: R" R the f function J must be at least: Select one: a. Infinitely differentiable b. Not everywhere zero C. Continuous d. Once differentiable e. None of the other options listed (B). Lagrange multipliers A (single) Lagrange multiplier arises from the requirement that Select one: a. a cross product is nonzero b. two numbers are proportional C. two square matrices are...
With justification in each one. Clarification; why if true and why if false? Please Determine whether the following statement is true or false: • Iff: R+R is differentiable and strictly increasing on R, then f'(1) > 0 VI ER • If S: R R is continuous and f(x) - ron Q, then (V3) - 3. • If f,g: (0,1) - Rare functions such that \S(1)-f(y) = g(1)-9(y) for all 1, y € (0, 1) and g is continuous on (0,1),...
(1 point) Enter a Tor an F in each answer space below to indicate whether the corresponding statement is true or false. A good technique is to think of several examples especially examples which might show that the statement is false! You must get all of the answers correct to receive credit. 1. Every differentiable function on the interval (4,5) must have both a maximum and a minimum 2. Every differentiable function on the interval (-3,0) must have a minimum....
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...
True or False Evaluate each of the statements below as true or false. a) A critical number of a function f(x) can only be defined as a number c in the domain of f(x) where f'(c) = 0). b) If f(x) is a continuous function on [a,b], then an absolute maximum ſ(c) and an absolute minimum f(d) for some c, d in [a, b] are guaranteed to exist. c) If f'(c) = 0, then f has a local maximum or a local minimum at...
Question 6 (1 point) Suppose a function f(x) is differentiable everywhere and has a local minimum at x=c. If f(x)<O when x<c, and f'(x)>0 when x>c, then by the Global Interval Method we know x=c is O a local maximum an absolute maximum a local minimum an absolute minimum
10. (18 points total: 3 points for each correct answer, 0 points for incorrect answers or no answer Answer "True" or "False” for each of the following: (i) If 8,9:R + R and are both continuous at a number c, then the composition function fog is continuous at c. (ii) If functions hi, h2: R + R and are both uniformly continuous on a non-empty set of real numbers E, then the product h h2 is uniformly continuous on E....
2. Indicate which species are aromatic by circling them. [4 points] 3. Predict the product(s) obtained in the following electrophilic aromatic substitution reactions. 12 points each] o HNO3 њео, F: d) Br2 Fsc FeBr3 a) Cl H2N e) H2S04 b) AICl3 H3CO c) Cl AICl3
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