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Secant/Tangent Lines and Limits

Secant/Tangent Lines and Limits

Assessment

Presentation

•

Mathematics

•

9th Grade

•

Medium

•
CCSS
HSF.IF.A.2, HSF-IF.C.7E, HSF-IF.C.7D

+1

Standards-aligned

Created by

Stanley Walerski

Used 8+ times

FREE Resource

23 Slides • 17 Questions

1

Lesson 2-5 Review

Tangent Lines and Limits

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2

Secant Line

3

Multiple Choice

Given  f(x)=x2−2xf\left(x\right)=x^2-2x  , find the slope of the secant line between x=-3 and x=9.

1

44  

2

−4-4  

3

14\frac{1}{4}  

4

−1-1  

4

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5

Tangent Line

6

Multiple Choice

If f(x)=x2−3xf\left(x\right)=x^2-3x , find the slope of the tangent line at  x=2x=2 .

1

2

2

-3

3

1

4

3

7

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8

Multiple Choice

If f(x)=x2−3xf\left(x\right)=x^2-3x , find the equation of the tangent line at  x=2x=2 . (Remember that  mtan⁡=1m_{\tan}=1  )

1

y + 2=(x−2)y\ +\ 2=\left(x-2\right)  

2

y=x−2y=x-2  

3

y=xy=x  

4

y−2=(x+2)y-2=\left(x+2\right)  

9

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10

Limits Graphically

11

Multiple Choice

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Find lim⁡x→0−f(x)\lim_{x\rightarrow0-}f\left(x\right)  .

1

0

2

-5

3

-6

4

Does Not Exist

12

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13

Multiple Choice

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Find lim⁡x→0+f(x)\lim_{x\rightarrow0+}f\left(x\right)  .

1

0

2

-5

3

-6

4

Does Not Exist

14

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15

Multiple Choice

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Find lim⁡x→0f(x)\lim_{x\rightarrow0}f\left(x\right)  .

1

0

2

-5

3

-6

4

Does Not Exist

16

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17

Multiple Choice

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Find  f(0)f\left(0\right)  

1

0

2

-5

3

-6

4

Does Not Exist

18

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19

Multiple Choice

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Find lim⁡x→5f(x)\lim_{x\rightarrow5}f\left(x\right)  .

1

0

2

-5

3

-6

4

Does Not Exist

20

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21

Multiple Choice

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lim⁡x→∞f(x)=\lim_{x\rightarrow\infty}f\left(x\right)=  

1

−∞-\infty  

2

∞\infty  

3

00  

4

DNEDNE  

22

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23

Multiple Choice

Question image

Given the graph, find lim⁡x→−∞f(x)\lim_{x\rightarrow-\infty}f\left(x\right)  .

1

+∞+\infty  

2

−∞-\infty  

3

7

4

-5

24

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25

Multiple Choice

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Given the graph, find lim⁡x→∞f(x)\lim_{x\rightarrow\infty}f\left(x\right)  .

1

+∞+\infty  

2

−∞-\infty  

3

2

4

8

26

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27

Limits Algebraically

To determine a limit algebraically as x approaches a specific value a...

1.  Substitute a into f(x)
2. Simplify/cancel factors, then substitute
3. Test left and right side limits (vertical asymptote)
4. Indeterminate

28

Limits Algebraically

To determine a limit algebraically as x approaches +/- infinity...

1.  Highest power in numerator (Top Heavy) = +/- infinity


2. Highest power the same in numerator/denominator (Balanced) = the ratio of the lead coefficients.

3. Highest power in the denominator (Bottom Heavy) = 0

29

Multiple Choice

Question image
1

0

2

1

3

8

4

DNE

30

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31

Multiple Choice

Question image
1

0

2

∞\infty

3

−∞-\infty

4

DNE

32

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33

Multiple Choice

Question image
1

0

2

1/2

3

∞\infty

4

−∞-\infty

34

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35

Multiple Choice

Question image
1

0

2

−45-\frac{4}{5}

3

∞\infty

4

−∞-\infty

36

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37

Multiple Choice

Question image
1

00

2

25\frac{2}{5}

3

∞\infty

4

−∞-\infty

38

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39

Multiple Choice

Question image

What is the limit of h(x) as x approaches -4?

1

1616

2

44

3

−4-4

4

DNEDNE

40

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pattern-tertiary
Lesson 2-5 Review

Tangent Lines and Limits

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