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  5. 2.1 Calc Difference Quotient

2.1 calc difference quotient

Authored by Erin Martin

Mathematics

9th - 12th Grade

CCSS covered

Used 3+ times

2.1 calc difference quotient
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18 questions

Show all answers

1.

LABELING QUESTION

1 min • 1 pt

Label the limit of the difference quotient

a
b
c
d
e
h→xh\rightarrow x
− f(x)-\ f\left(x\right)
h→0h\rightarrow0
+ f(x)+\ f\left(x\right)
f(x+h)f\left(x+h\right)
x→0x\rightarrow0
lim
x
h→∞h\rightarrow\infty
h

2.

LABELING QUESTION

1 min • 1 pt

Label the limit of the difference quotient for f(x) = 2x2 + 1

a
b
c
d
e
2x+h2+12x+h^2+1
+ (2x2+1)+\ \left(2x^2+1\right)
2(x+h)2+12\left(x+h\right)^2+1
− (2x2+1)-\ \left(2x^2+1\right)
h→∞h\rightarrow\infty
lim
x→0x\rightarrow0
h→0h\rightarrow0
h

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.APR.A.1

3.

LABELING QUESTION

1 min • 1 pt

Label the limit of the difference quotient for f(x) = x3 - 3x

a
b
c
d
e
+ (x3−3x)+\ \left(x^3-3x\right)
x→0x\rightarrow0
h→0h\rightarrow0
x3 − 3(x + h)x^3\ -\ 3\left(x\ +\ h\right)
(x+h)3 − 3x\left(x+h\right)^{3\ }-\ 3x
h→∞h\rightarrow\infty
lim
(x+h)3−3(x+h)\left(x+h\right)^3-3\left(x+h\right)
h
− (x3−3x)-\ \left(x^3-3x\right)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.1

4.

LABELING QUESTION

1 min • 1 pt

Label the limit of the difference quotient for f(x) = 2x - 1

a
b
c
d
e
2(x + h) − 12\left(x\ +\ h\right)\ -\ 1
2x + h − 12x\ +\ h\ -\ 1
2(x + h) − (x + h)2\left(x\ +\ h\right)\ -\ \left(x\ +\ h\right)
lim
h→0h\rightarrow0
h→∞h\rightarrow\infty
x→0x\rightarrow0
− (2x − 1)-\ \left(2x\ -\ 1\right)
h
+ (2x−1)+\ \left(2x-1\right)

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

5.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the average rate of change of f(x)=−2x2+4x+6f\left(x\right)=-2x^2+4x+6  from [-3, -1].

10

12

14

16

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

f(x)=x+8+2f\left(x\right)=\sqrt{x+8}+2  
Evaluate  f(x−8)f\left(x-8\right)  

2

x2−8+2\sqrt{x^2-8}+2  

0

x+2\sqrt{x}+2  

Tags

CCSS.HSF.IF.A.2

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

h(t)=t2−2th\left(t\right)=t^2-2t  
Evaluate  h(x+2)h\left(x+2\right)  

x(x+2)x\left(x+2\right)  

x(x−2)x\left(x-2\right)  

t2−2t+2t^2-2t+2  

t(t−2)t\left(t-2\right)  

Tags

CCSS.HSF.IF.A.2

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