Limit Process and Infinity

Limits process and Infinity Drills
Grade 12

Basic Calculus

Objectives

Limits

The idea of limits is fundamental to the study of calculus. It suggests a boundary that may be reached or not, or possibly exceeded. A mathematical limit has characteristics similar to those of a physical limit. It is the analysis of how function values or outputs change, when inputs change.

Limits

Limits

Multiple Choice

What is the limit of  $$\lim_{x\rightarrow-1}\left(x^2+1\right)$$  ?

• 1

• 2

• 3

• 4

Multiple Choice

Find  $$\lim_{x\rightarrow0}\frac{x^2-4x+8}{x-2}$$ . 

• 0

• 4

• -4

• d.n.e.

Multiple Choice

What is the $$\lim_{x\rightarrow-5}\ \frac{x^2-25}{x+5}$$  ?

• d.n.e.

• 5

• 10

• -10

Multiple Choice

• Does not exist
• -7/5
• -5/9
• -1/2

Multiple Choice

$$\lim_{x\rightarrow3}\ \frac{x^2-9}{x^2-5x+6}=....$$  

• $$-6$$  

• $$-3$$  

• $$0$$  

• $$3$$  

• $$6$$  

Multiple Choice

$$\lim_{x\rightarrow-3}\ \ \frac{x+3}{x^2-9}\ =\ ....$$  

• 0

• $$-6$$

• 6

• $$-\frac{1}{6}$$  

• $$\frac{1}{6}$$  

Multiple Choice

$$\lim_{x\rightarrow2}\ \ \frac{x^3-8}{x-2}\ =\ ....$$  

• 0

• $$\infty$$  

• 12

• $$-12$$  

• $$\frac{1}{12}$$  

Multiple Choice

$$\lim_{x\rightarrow-5}\ \ \ \frac{x+5}{2}\ =\ ....$$  

• 0

• 5

• $$\infty$$  

• $$\frac{5}{2}$$  

• $$\frac{2}{5}$$  

Multiple Choice

$$\lim_{x\rightarrow4}\ \ \frac{x^2-3x-4}{5x-20}\ =\ ....$$  

• 1

• 21

• 20

• 19

• 0

Multiple Choice

What is the limit?

• DNE
• Infinity
• 6
• 12

Multiple Choice

$$\lim_{x\rightarrow2}\ \left(x^2+2x-3\right)\ =.......$$  

• 3

• 4

• 5

• 6

• 7

Multiple Choice

$$\lim_{x\rightarrow3}\ \frac{x^2\ -8x\ +15}{x-3}=..............$$  

• 3

• -2

• -3

• -6

• -7

Multiple Choice

$$\lim_{x\rightarrow16}\ \frac{\sqrt{x}-4}{x\ -\ 16}\ =........$$  

• 0

• $$\frac{1}{8}$$  

• $$\frac{1}{4}$$  

• $$\frac{1}{2}$$  

• $$\infty$$  

Multiple Choice

$$\lim_{x\rightarrow1}\ \left(\frac{x-2}{x+3}\right)\ =........$$  

• $$-\frac{2}{3}$$  

• $$-\frac{1}{4}$$  

• $$\frac{1}{2}$$  

• $$\frac{2}{3}$$  

• 1

Fill in the Blanks

$\lim_{x\rightarrow-\infty}\frac{3x^2+2x^3+x-7}{x^3-3x+5}=$  

Multiple Choice

$$\lim_{x\rightarrow+\infty}\frac{5x^4-3x^3+9}{4x^4-2x^2+x-1}=\$$  

• $$0$$  

• $$\frac{5}{4}$$  

• $$+\infty$$  

• $$DNE$$  

Fill in the Blanks

$\lim_{x\rightarrow-\infty}\frac{-8x^2-6x+4}{4x^4+9x^3-8}=$  

Multiple Choice

$$\lim_{x\rightarrow+\infty}\frac{-6x^2+9x-2}{3x^2-x+1}=$$  

• $$0$$  

• $$-2$$  

• $$+\infty$$  

• $$-\infty$$  

Multiple Choice

Find the limit

• ³/₄

• 0

• ∞

• -∞

Multiple Choice

Find the limit

• ⁶/₅

• 0

• ∞

• -∞

Multiple Choice

Evaluate $$\lim_{x\rightarrow\infty}\left(\frac{6x^5-9x^3+12x^2-10}{x+5x^3-x^5}\right)$$  .

• $$\infty$$  

• $$-\infty$$  

• -6

• 6

Multiple Choice

Solve $$\lim_{x\rightarrow-\infty}\left(\frac{1-x}{1-x^2}\right)$$  .

• $$\infty$$  

• $$-\infty$$  

• Does not exist

• 0

Multiple Choice

Find the limit. 

• ³/₇

• 0

• $$\infty$$

• $$-\infty$$
  

Multiple Choice

Determine the limit at infinity .
$$\lim_{x\rightarrow\infty}\left(\frac{x^2-x-12}{x+3}\right)$$  

• $$\infty$$  

• $$-\infty$$  

• -3

• 4

Multiple Choice

$$\lim_{y\rightarrow\infty}\left(\frac{2y^2+y-5}{4y^2+5y+2}\right)$$  

• 1/2

• $$\infty$$  

• 2

• -1

Multiple Choice

$$\lim_{x\rightarrow\infty}\ \frac{x^3-x^2+1}{5-3x-x^4}=...$$  

• 0

• -1

• -5

• $$\infty$$   

• $$-\infty$$