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3.5 of 1 2 3 4 5 For each expression below, calculate its value if it...
1. (3 points each) Answer each of the following statements as true or false a. If lim ) exists, t...
1. (3 points each) Answer each of the following statements as true or false a. If lim ) exists, then lim(lim() b. If lim f (x) exists, then fi (zo) exists. c. If f differentiable on la, b, then f is integrable on [a, b]. d. If f is continuous on [a, b] and differentiable on (a, b), then there exists a number X -To (a, b) such that f (b) f(a)- (b-a)f (x). e. If f is integrable on...
For part (a), please prove the answer. 5. Let S = {1, 2, 3, 4} and...
For part (a), please prove the answer.
5. Let S = {1, 2, 3, 4} and let F be the sets of all functions from S to S. Let R be the relation on F defined by: For all f,g EF, fRg if and only if fog(1)-2. (a) Is R reflexive? symmetric? transitive? (b) Is it true that that there exists f E F so that fRf? Prove your answer. (c) Is it true that for all f F, there...
4 -2 2. The function f is defined on the closed interval [-4,9]. The graph of...
4 -2 2. The function f is defined on the closed interval [-4,9]. The graph of f consists of a semicircle, a quarter circle, and three linear segments, as shown in the figure above. Let g be the function defined by g(x) = 3x + f(t) dt. (a) Find g(8) and g'(8). (b) Find the value of x in the closed interval (-4,9] at which g attains its maximum value. Justify your answer. (c) Find lim f'(x), or state that...
help me to solve this question please ( real analysis ) 1. For each of the...
help me to solve this question please
( real analysis )
1. For each of the following use Theorem 3.3.4 to determine if the limit exists and the value of the limit when it does exist. (d) lim 1-40 |+2 (b) lim VH (e) lim / +2 ( limsin Theorem 3.3.4. Suppose f is defined in a deleted neighborhood of a point c. Then lim-f(x) exists and equals Lif and only if both lim + f(x) and lim- f(x) exist...
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3...
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3 x2 -9x + 20 Evaluate the following limits You do not have to cite limit laws, but you must show how you arrived at your answer If a limit Does Not Exist, explain why. You should use oo or -oo where applicable Calculating the limit using L'Hopital's Rule will receive NO CREDIT. (a) lim f(x) r-+0 (b) lim f(x)= z-1 (e) lim f(z) (d)...
6. Consider the autonomous differential equation (a) Find all of its equilibrium solutions. (b) Classify the stability of each equilibrium solution. Justify your answer. (c) If y(t) is a solution tha...
6. Consider the autonomous differential equation (a) Find all of its equilibrium solutions. (b) Classify the stability of each equilibrium solution. Justify your answer. (c) If y(t) is a solution that satisfies y(-1) =-4, what is y(0)? Without solving the equation, briefly explain your conclusion. (d) If y() is a solution that satisis y(3) -3, then what is lim y(t)?
6. Consider the autonomous differential equation
(a) Find all of its equilibrium solutions. (b) Classify the stability of each equilibrium...
1. Consider the following matrices. A= 1 2 -1 0 3 4 B 2 3-4 5...
1. Consider the following matrices. A= 1 2 -1 0 3 4 B 2 3-4 5 1 and C= -[-1:] Compute each of the following, if it is defined. If an expression is undefined, explain why. (a) (4 points) A+B (b) (4 points) 2B (c) (4 points) AC (d) (4 points) CB
A) For the following scores, find the value of each expression: X 3 5 O 2...
A) For the following scores, find the value of each expression: X 3 5 O 2 1. Σx 2. Σx2 3. ΣΧ+1 4. Σ (Χ+1) B. For the following set of scores, find the value of each expression: X 3 2. 5 1 3 1. x2 2. (2x) 3. (X-1) 4. (x-1)2 C) For the following set of scores, find the value of each expression: X 6 -2 0 -3 -1 1. Ex 2. x2 3. (X+3) D) For the...
4. [-12.94 Points) DETAILS SPRECALC7 6.4.006. Find the exact value of each expression, if it is...
4. [-12.94 Points) DETAILS SPRECALC7 6.4.006. Find the exact value of each expression, if it is defined. Express your answer in radians. (If an answer is undefine (a) sin-20) (b) cos(-1) (c) tan-(0) 5. (-/2.94 Points] DETAILS SPRECALC7 6.4.031. Find the exact value of the expression. sedsin-::-))
For each of the languages listed below, give a regular expression that generates the lan- guage....
For each of the languages listed below, give a regular expression that generates the lan- guage. Briefly justify your answer. (a) The set of strings over (a, b such that any a in the string is followed by an odd number of b's. Examples: bbbab E L, but abb f L. (b) The set of strings over fa, b in which there is an a in every even position and the total number of b's is odd, where the first...
1. (3 points each) Answer each of the following statements as true or false a. If lim ) exists, then lim(lim() b. If lim f (x) exists, then fi (zo) exists. c. If f differentiable on la, b, then f is integrable on [a, b]. d. If f is continuous on [a, b] and differentiable on (a, b), then there exists a number X -To (a, b) such that f (b) f(a)- (b-a)f (x). e. If f is integrable on...
For part (a), please prove the answer.
5. Let S = {1, 2, 3, 4} and let F be the sets of all functions from S to S. Let R be the relation on F defined by: For all f,g EF, fRg if and only if fog(1)-2. (a) Is R reflexive? symmetric? transitive? (b) Is it true that that there exists f E F so that fRf? Prove your answer. (c) Is it true that for all f F, there...
4 -2 2. The function f is defined on the closed interval [-4,9]. The graph of f consists of a semicircle, a quarter circle, and three linear segments, as shown in the figure above. Let g be the function defined by g(x) = 3x + f(t) dt. (a) Find g(8) and g'(8). (b) Find the value of x in the closed interval (-4,9] at which g attains its maximum value. Justify your answer. (c) Find lim f'(x), or state that...
help me to solve this question please
( real analysis )
1. For each of the following use Theorem 3.3.4 to determine if the limit exists and the value of the limit when it does exist. (d) lim 1-40 |+2 (b) lim VH (e) lim / +2 ( limsin Theorem 3.3.4. Suppose f is defined in a deleted neighborhood of a point c. Then lim-f(x) exists and equals Lif and only if both lim + f(x) and lim- f(x) exist...
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3 x2 -9x + 20 Evaluate the following limits You do not have to cite limit laws, but you must show how you arrived at your answer If a limit Does Not Exist, explain why. You should use oo or -oo where applicable Calculating the limit using L'Hopital's Rule will receive NO CREDIT. (a) lim f(x) r-+0 (b) lim f(x)= z-1 (e) lim f(z) (d)...
6. Consider the autonomous differential equation (a) Find all of its equilibrium solutions. (b) Classify the stability of each equilibrium solution. Justify your answer. (c) If y(t) is a solution that satisfies y(-1) =-4, what is y(0)? Without solving the equation, briefly explain your conclusion. (d) If y() is a solution that satisis y(3) -3, then what is lim y(t)?
6. Consider the autonomous differential equation
(a) Find all of its equilibrium solutions. (b) Classify the stability of each equilibrium...
1. Consider the following matrices. A= 1 2 -1 0 3 4 B 2 3-4 5 1 and C= -[-1:] Compute each of the following, if it is defined. If an expression is undefined, explain why. (a) (4 points) A+B (b) (4 points) 2B (c) (4 points) AC (d) (4 points) CB
A) For the following scores, find the value of each expression: X 3 5 O 2 1. Σx 2. Σx2 3. ΣΧ+1 4. Σ (Χ+1) B. For the following set of scores, find the value of each expression: X 3 2. 5 1 3 1. x2 2. (2x) 3. (X-1) 4. (x-1)2 C) For the following set of scores, find the value of each expression: X 6 -2 0 -3 -1 1. Ex 2. x2 3. (X+3) D) For the...
4. [-12.94 Points) DETAILS SPRECALC7 6.4.006. Find the exact value of each expression, if it is defined. Express your answer in radians. (If an answer is undefine (a) sin-20) (b) cos(-1) (c) tan-(0) 5. (-/2.94 Points] DETAILS SPRECALC7 6.4.031. Find the exact value of the expression. sedsin-::-))
For each of the languages listed below, give a regular expression that generates the lan- guage. Briefly justify your answer. (a) The set of strings over (a, b such that any a in the string is followed by an odd number of b's. Examples: bbbab E L, but abb f L. (b) The set of strings over fa, b in which there is an a in every even position and the total number of b's is odd, where the first...
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