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Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Limits and continuity

Grade: 1400-a Lesson: S2-L4

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: in Class

Problem Id	Problem	Options
1	Find the limit or state that it does not exist: \$lim_(x->0) ((x^2 + x - 20) / (x - 4))\$.	A) 10 B) 12 C) 9 D) 15
2	Compute \$lim_(x->0)( (2x^2 + 3x + 4) / x) + ((5x - 4) / x)\$.	A) 5 B) 4 C) 6 D) 8
3	Compute \$lim_(h->0) ((h + 4)^2 - 16) / h\$.	A) 10 B) 8 C) 12 D) 14
4	Find the limit \$lim_(t->0^(+)) (\sqrtt^3 / \sqrtt)\$.	A) 0 B) 1 C) 2 D) 3
5	Find the limit \$lim_(x->∞) ((x^2 + x + 1) / (3x + 2)^2)\$.	A) \$1 / 9\$ B) \$1 / 3\$ C) 0 D) 1
6	Find the horizontal and vertical asymptotes of \$ f(x) = (3x^2-9x)/ (x^2-9) \$.	A) Horizontal Asymptote: y = 3 Vertical Asymptotes: x = ± 4 B) Horizontal Asymptote: y = 3 Vertical Asymptotes: x = ± 3 C) Horizontal Asymptote: y = 3 Vertical Asymptotes: x = 3 D) Horizontal Asymptote:y = 4 Vertical Asymptotes: x = ± 3
7	\$lim_(x->0) (tanx - x)/(x^3)\$.	A) \$2 / 3\$ B) \$1 / 3\$ C) \$5 / 3\$ D) \$1 / 2\$
8	Determine if the function \$f(x) = sqrt(x + 4)\$ is continuous at x = - 4.	A) 8 B) -8 C) Continuous D) Not continuous
9	Limit of \$(4x^2 - 3x - 5) / (6x^2 +9x - 3)\$ as x approaches 4:	A) \$ 34 / 111 \$ B) \$ 45 / 119 \$ C) \$ 47 / 129 \$ D) \$ 40 / 132\$
10	Find the x-values for which \$"f(x)" = 2/(sqrt(1 - x))\$ continuous.	A) (∞, 4) B) (−∞, 3) C) (∞, 2) D) (−∞, 1)

Problem Id

Problem

Options

Find the limit or state that it does not exist: \$lim_(x->0) ((x^2 + x - 20) / (x - 4))\$.

A) 10

B) 12

C) 9

D) 15

Compute \$lim_(x->0)( (2x^2 + 3x + 4) / x) + ((5x - 4) / x)\$.

A) 5

B) 4

C) 6

D) 8

Compute \$lim_(h->0) ((h + 4)^2 - 16) / h\$.

A) 10

B) 8

C) 12

D) 14

Find the limit \$lim_(t->0^(+)) (\sqrtt^3 / \sqrtt)\$.

A) 0

B) 1

C) 2

D) 3

Find the limit \$lim_(x->∞) ((x^2 + x + 1) / (3x + 2)^2)\$.

A) \$1 / 9\$

B) \$1 / 3\$

C) 0

D) 1

Find the horizontal and vertical asymptotes of \$ f(x) = (3x^2-9x)/ (x^2-9) \$.

A) Horizontal Asymptote: y = 3 Vertical Asymptotes: x = ± 4

B) Horizontal Asymptote: y = 3 Vertical Asymptotes: x = ± 3

C) Horizontal Asymptote: y = 3 Vertical Asymptotes: x = 3

D) Horizontal Asymptote:y = 4 Vertical Asymptotes: x = ± 3

\$lim_(x->0) (tanx - x)/(x^3)\$.

A) \$2 / 3\$

B) \$1 / 3\$

C) \$5 / 3\$

D) \$1 / 2\$

Determine if the function \$f(x) = sqrt(x + 4)\$ is continuous at x = - 4.

A) 8

B) -8

C) Continuous

D) Not continuous

Limit of \$(4x^2 - 3x - 5) / (6x^2 +9x - 3)\$ as x approaches 4:

A) \$ 34 / 111 \$

B) \$ 45 / 119 \$

C) \$ 47 / 129 \$

D) \$ 40 / 132\$

Find the x-values for which \$"f(x)" = 2/(sqrt(1 - x))\$ continuous.

A) (∞, 4)

B) (−∞, 3)

C) (∞, 2)

D) (−∞, 1)