$$\lim_{x \to a} f(x)$$ does not exist

Question 1

Given the function $$f(x) = x^2$, what is $$\lim_{x 	o \infty} f(x)$$?

Accepted Answer

$$\infty$$

Question 2

For the function $$f(x) = \frac{2}{x}$$, what is $$\lim_{x 	o \infty} f(x)$$?

Accepted Answer

$$0$$

Question 3

If $$\lim_{x 	o a^-} f(x) = 3$$ and $$\lim_{x 	o a^+} f(x) = 5$$, what can you conclude about $$\lim_{x 	o a} f(x)$$?

Accepted Answer

$$\lim_{x 	o a} f(x)$$ does not exist

Question 4

Given the graph of $$f(x)$$ with $$f(0) = 1$$ and $$\lim_{x 	o 0} f(x) = 2$$, which statement is true?

Accepted Answer

There is a removable discontinuity at $$x=0$$

Question 5

Evaluate $$\lim_{x 	o 0} \frac{1}{x}.$$

Accepted Answer

Does not exist

Question 6

If $$\lim_{x 	o a^-} f(x) = L$$ and $$\lim_{x 	o a^+} f(x) = L$$, what must be true for $$\lim_{x 	o a} f(x) to $$exist?

Accepted Answer

Both one-sided limits must exist and be equal

Question 7

Given $$\lim_{x 	o 2} f(x) = 0$$ and $$\lim_{x 	o 2} g(x) = -\frac{1}{2}$$, what is $$\lim_{x 	o 2} [f(x) + g(x)]$$?

Accepted Answer

$$-\frac{1}{2}$$

Question 8

Suppose $$\lim_{x 	o \infty} 4x + 1 is $$evaluated. What is the result?

Accepted Answer

$$\infty$$

Question 9

If $$\lim_{x 	o 0} x^3$ = 0$$, what is $$\lim_{x 	o 0} x^5$?

Accepted Answer

$$0$$

Question 10

Given the graph of $$f(x)$$, if $$\lim_{x 	o -1} f(x) = 1$$ and $$f(-1) = 1$$, what does this indicate about the function at $$x = -1$$?

Accepted Answer

The function is continuous at $$x = -1$$

Question 11

If $$\lim_{x 	o 0} f(x) = \infty$$, which of the following is true?

Accepted Answer

The function grows without bound as $$x$$ approaches $$0$$

Question 12

Evaluate $$\lim_{x 	o 0} 10.$$

Accepted Answer

$$10$$

Question 13

If $$\lim_{x 	o a} f(x)$$ does not exist, which of the following could be a reason?

Accepted Answer

The left and right limits at $$x=a$$ are not equal

Question 14

Given $$\lim_{x 	o 0} x = 0$$, what is $$\lim_{x 	o 0} 4x$$?

Accepted Answer

$$0$$

Question 15

If $$\lim_{x 	o 0} f(x) = 2$$ and $$\lim_{x 	o 0} g(x) = 3$$, what is $$\lim_{x 	o 0} [f(x) + g(x)]$$?

Accepted Answer

$$5$$

Question 16

Suppose $$\lim_{x 	o 0} f(x) = \infty$$ and $$\lim_{x 	o 0} g(x) = -\infty. $$What is $$\lim_{x 	o 0} [f(x) + g(x)]$$?

Accepted Answer

Does not exist

Question 17

If $$\lim_{x 	o a} f(x) = L$$ and $$f(a) 
eq L$$, what type of discontinuity is present at $$x=a$$?

Accepted Answer

Removable discontinuity

Question 18

Evaluate $$\lim_{x 	o 0} x^3$.

Accepted Answer

$$0$$

Question 19

If $$\lim_{x 	o 0^-} f(x) = -1$$ and $$\lim_{x 	o 0^+} f(x) = 1$$, what is $$\lim_{x 	o 0} f(x)$$?

Accepted Answer

Does not exist

Question 20

Given $$\lim_{x 	o \infty} x = \infty$$, what is $$\lim_{x 	o \infty} (4x + 1)$$?

Accepted Answer

$$\infty$$

Limits and Their Properties in Business Calculus

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