Question

In: Math

Determine whether the statement is true or false. If it is false, explain why or give...

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If f(c) = L,then lim x→c f(x) = L.

False. Define f to be the piece-wise function where f(x) = x + 3 when x ≠ −1 and f(x) = 2 when x = −1. Then we have f(−1) = 2 while the limit of f as x approaches −1 is equal to −2.

False. Define f to be the piece-wise function where f(x) = x − 4 when x ≠ 2 and f(x) = 0 when x = 2. Then we have f(2) = 0 while the limit of f as x approaches 2 is equal to −2.

False. If f(c) = L, then the limit of f as x approaches c is equal to L/c.

False. If f(c) = L, then the limit of f as x approaches c is equal to cL.

The statement is true.

Solutions

Expert Solution

If f(c) =L then    it is (False)

We can see by an example -

Here

  

So these are not equal.

   Define f to be the piece-wise function where f(x) = x + 3 when x ≠ −1 and f(x) = 2 when x = −1. Then we have f(−1) = 2 while the limit of f as x approaches −1 is equal to −2. (False )

Define f to be the piece-wise function where f(x) = x − 4 when x ≠ 2 and f(x) = 0 when x = 2. Then we have f(2) = 0 while the limit of f as x approaches 2 is equal to −2. (True)

And

If f(c) = L, then the limit of f as x approaches c is equal to L/c. (False) There is no relation between these.

False. If f(c) = L, then the limit of f as x approaches c is equal to cL. (False) There is no relation between these.

  

  


Related Solutions

True or False. Indicate whether the statement is true or false. If false, explain in the...
True or False. Indicate whether the statement is true or false. If false, explain in the space provided the statement why it is false, or simply correct the statement. Smooth muscle contraction is regulated by the autonomic nervous system. During exercise, the sympathetic nerves that innervate the smooth muscles of bronchioles and arterioles regulate the contraction of these smooth muscles to increase ventilation and cardiac output. 2. Multiple choice: Choose one best statement. An infant born prematurely has neonatal respiratory...
True/False (3 pts each) Indicate whether the statement is true or false. If true, explain why...
True/False (3 pts each) Indicate whether the statement is true or false. If true, explain why it is true and/or give examples to support it. If false, explain why it is false. 2.​An increase in plasma osmolality will cause more secretion of ADH.
For each statement, determine whether the statement is true or false. Give a sentence justifying your answer.
For each statement, determine whether the statement is true or false. Give a sentence justifying your answer. a. If tan(t)=0, then cos(t)=1 . b. The function f(x)=sin(x)cos(x) has period 2π. c. The graph of r = 1 is the unit circle. d. Two angles with the same cosine value must have the same sine value. e. The point (0, -3) in Cartesean coordinates can also be described by the ordered pair (-3, π/2) in polar coordinates
Indicate whether the statement is true or false. If false, please explain why. (Note that if...
Indicate whether the statement is true or false. If false, please explain why. (Note that if the explanation is incomplete, you may not get the full credits.) a. Although payroll taxes are imposed on firms, workers bear more burdens than firms when the elasticity of labor supply is greater than the elasticity of labor demand. (4 pts) b. There might be a situation in which dangerous jobs offer lower wages than safe jobs even if there exist compensating wage differentials....
Determine whether each statement is true or false. If it is true, prove it. If it...
Determine whether each statement is true or false. If it is true, prove it. If it is false, give a counterexample. a) For every function f : X → Y and all A ⊆ X, we have f^−1 [f[A]] = A. (b) For every function f : X → Y and all A ⊆ X, we have f[X \ A] = Y \ f[A]. (c) For every function f : X → Y and all A, B ⊆ Y ,...
Determine whether each of the following statements is true or false, and explain why in a...
Determine whether each of the following statements is true or false, and explain why in a few sentences. 1. The mean, median, and mode of a normal distribution are all equal. 2. If the mean, median, and mode of a distribution are all equal, then the distribution must be a normal distribution. 3. If the means of two distributions are equal, then the variance must also be equal. 4. The sample mean is not the same as the population mean....
State whether the following statement is true or false AND explain why: "An increase in the...
State whether the following statement is true or false AND explain why: "An increase in the interest rate paid on excess reserves will always cause an increase in the federal reserve funds rate."
Determine whether each of the following statements is true or false. If the statement is false,...
Determine whether each of the following statements is true or false. If the statement is false, modify and rewrite it so that it is a true statement. a. When a molecule has two, degenerate, “infrared active”, vibrational modes, the two vibrational modes will show absorptions at different frequencies in the infrared spectrum. b. For a given substance, strong intermolecular forces between molecules of the substance can cause peak broadening of some of the absorptions in the infrared spectrum of the...
Determine whether the following statements are true or false and explain why. a. An upward sloping...
Determine whether the following statements are true or false and explain why. a. An upward sloping demand curve implies a downward sloping Engel curve. b. In a world with only two goods, good A and good B, if the Engel curve for good A is downward sloping, then good B is a normal good for sure.
Evaluate whether the statement is true or false. Explain why. a. Dominant strategy equilibrium is a...
Evaluate whether the statement is true or false. Explain why. a. Dominant strategy equilibrium is a Nash equilibrium. b. A Nash equilibrium is Pareto efficient. c. Every subgame perfect Nash equilibrium is a Nash equilibrium.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT