Question 1

Suppose $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2. $$What is $$\lim\limits_{x 	o 3} (f(x) + 7g(x))$$?

Accepted Answer

$$5 + 7(-2) = -9$$

Question 2

Given $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2$$, evaluate $$\lim\limits_{x 	o 3} \dfrac{f(x)}{\sqrt{f(x)} + g(x)^2$}.$$

Accepted Answer

$$\dfrac{5}{\sqrt{5} + 4}$$

Question 3

If $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2$$, what is $$\lim\limits_{x 	o 3} (2f(x) - 3g(x))$$?

Accepted Answer

$$2 \cdot 5 - 3 \cdot (-2) = 10 + 6 = 16$$

Question 4

Suppose $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2. $$What is $$\lim\limits_{x 	o 3} (f(x)g(x))$$?

Accepted Answer

$$-10$$

Question 5

Given $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2$$, evaluate $$\lim\limits_{x 	o 3} \dfrac{f(x) + g(x)}{f(x) - g(x)}.$$

Accepted Answer

$$\dfrac{5 + (-2)}{5 - (-2)} = \dfrac{3}{7}$$

Question 6

If $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2$$, what is $$\lim\limits_{x 	o 3} (f(x)^2$ + g(x)^2$)$$?

Accepted Answer

$$5^2$$ + $$(-2)^2 = 25 + 4 = 29$

Question 7

Suppose $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2. $$What is $$\lim\limits_{x 	o 3} \sqrt{f(x) + g(x)}$$?

Accepted Answer

$$\sqrt{5 + (-2)} = \sqrt{3}$$

Question 8

Given $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2$$, evaluate $$\lim\limits_{x 	o 3} \dfrac{f(x)}{g(x)}.$$

Accepted Answer

$$-2.5$$

Question 9

If $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2$$, what is $$\lim\limits_{x 	o 3} (f(x) - g(x))^2$?

Accepted Answer

$$(5 - (-2))^2$ = (7)^2$ = 49$$

Question 10

Suppose $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2. $$What is $$\lim\limits_{x 	o 3} \dfrac{f(x)g(x)}{f(x) - g(x)}$$?

Accepted Answer

$$\dfrac{5 \cdot (-2)}{5 - (-2)} = \dfrac{-10}{7}$$

Question 11

Given $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2$$, evaluate $$\lim\limits_{x 	o 3} \dfrac{f(x) + g(x)}{g(x)^2$}.$$

Accepted Answer

$$\dfrac{5 + (-2)}{(-2)^2$} = \dfrac{3}{4}$$

Question 12

If $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2$$, what is $$\lim\limits_{x 	o 3} \dfrac{f(x)^2$}{g(x)}$$?

Accepted Answer

$$\dfrac{25}{-2} = -12.5$$

Question 13

Suppose $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2. $$What is $$\lim\limits_{x 	o 3} \dfrac{f(x) - g(x)}{f(x) + g(x)}$$?

Accepted Answer

$$\dfrac{5 - (-2)}{5 + (-2)} = \dfrac{7}{3}$$

Question 14

Given $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2$$, evaluate $$\lim\limits_{x 	o 3} \sqrt{f(x)} + |g(x)|.$$

Accepted Answer

$$\sqrt{5} + 2$$

Question 15

If $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2$$, what is $$\lim\limits_{x 	o 3} \dfrac{f(x)g(x)}{g(x)^2$}$$?

Accepted Answer

$$\dfrac{5 \cdot (-2)}{(-2)^2$} = \dfrac{-10}{4} = -2.5$$

Question 16

Suppose $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2. $$What is $$\lim\limits_{x 	o 3} (f(x) + g(x))^2$?

Accepted Answer

$$(5 + (-2))^2$ = (3)^2$ = 9$$

Question 17

Given $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2$$, evaluate $$\lim\limits_{x 	o 3} \dfrac{f(x) - g(x)}{g(x)}.$$

Accepted Answer

$$\dfrac{5 - (-2)}{-2} = \dfrac{7}{-2} = -3.5$$

Question 18

If $$\lim\limits_{x 	o 3} f(x) = 5$$ and $$\lim\limits_{x 	o 3} g(x) = -2$$, what is $$\lim\limits_{x 	o 3} \dfrac{f(x)}{g(x)^2$ + 1}$$?

Accepted Answer

$$\dfrac{5}{(-2)^2$ + 1} = \dfrac{5}{5} = 1$$

Limits and Limit Laws in Calculus: Study Notes

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