Limits (Using appropriate method)

Limits (Using appropriate method)

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Learning Outcomes

It means that the limit exists and is equal to L.

Now, it's time to test your knowledge

Multiple Choice

Find

$$\lim_{x\rightarrow2}\ \ \ x\left(x-1\right)\left(x+1\right)$$ . 

• 6

• 2

• 0

• -2

Fill in the Blank

Determine

$$\lim_{x\rightarrow3}\ \ \frac{x^2-2x}{x+1}$$  .

(type your answer without space)

Fill in the Blank

Find  $$\lim_{x\rightarrow9}\ \ \frac{x-9}{\sqrt{x}-3}$$  .

(type your answer without space)

Multiple Select

Compute $$\lim_{x\rightarrow3^-}\ \ \frac{3\left|x-3\right|}{x-3}$$  

• $$3$$  

• $$0$$  

• $$\infty$$  

• $$-3$$  

Fill in the Blank

$$f\left(x\right)$$  is a function given in the diagram. Write down  $$\lim_{x\rightarrow2^{-\ }}\ f\left(x\right)$$  

(type your answer without space)

Multiple Choice

If $$f\left(x\right)=\sqrt{x}$$  , then find  $$\lim_{h\rightarrow0}\ \ \ \left[\frac{f\left(x+h\right)-f\left(x\right)}{h}\right]$$  

• $$1$$  

• $$\frac{1}{\sqrt{x}}$$  

• $$\frac{1}{2\sqrt{x}}$$  

• $$-\frac{1}{\sqrt{x}}$$  

Fill in the Blank

$$f\left(x\right)$$  is a function given in the diagram. What is   $$\lim_{x\rightarrow6^{ }}\ \ f\left(x\right)$$  ?

(type your answer without space)

Fill in the Blank

$$f\left(x\right)$$  is a function given in the diagram. Find  $$\lim_{x\rightarrow8^+}\ \ f\left(x\right)$$  .

(type your answer without space)

Multiple Choice

 Do you think $$\lim_{x\rightarrow3}\ \ h\left(x\right)$$ exists?

• exist

• does not exist

Multiple Select

Find $$\lim_{x\rightarrow0}\ \ \left[\frac{\frac{1}{2+x}-\frac{1}{2}}{x}\right]$$  

• 0

• $$+\infty$$  

• $$-\frac{1}{4}$$  

• $$-\infty$$  

Fill in the Blank

$$f\left(x\right)$$  is a function given in the diagram. Find  $$\lim_{x\rightarrow8^+}\ \ f\left(x\right)$$  .

(type your answer without space)

Fill in the Blank

Evaluate the following: $$\lim_{x\rightarrow\left(-2\right)}\ \ x^3\left(7x^2+3x-1\right)$$ . 

(type your answers without space)

Multiple Select

Find

$$\lim_{x\rightarrow3^-}\ \ f\left(x\right)$$  

• 14

• 2

• 4

• 7

Multiple Choice

Given $$g\left(x\right)=\frac{5x^3+4}{x-3}$$ , find  $$\lim_{x\rightarrow2}\ \ g\left(x\right)$$  . 

• 44

• -44

• 24

• -24

Multiple Choice

Do you think that $$\lim_{x\rightarrow\left(-2\right)}\ \ h\left(x\right)$$ exists? 

• exist

• does not exist

Multiple Select

Find $$\lim_{x\rightarrow1}\ \left[\frac{x^2-6x+5}{x-1}\right]$$ . 

• $$+\infty$$  

• 0

• $$-4$$  

• $$-\infty$$  

Fill in the Blank

Find $$\lim_{x\rightarrow6}\ \left[\frac{\sqrt{x-2}-2}{x-6}\right]$$ .

(type your answer without space)