Unit 1 Flashcards

1
Q

1/x

A

x^-1

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2
Q

1/x^p

A

x^-p

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3
Q

√x

A

x^1/2

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4
Q

m√x^n

A

x^n/m

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5
Q

√(x^2)

A

|x|

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6
Q

(√x)^2

A

x

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7
Q

The instantaneous rate of change is the __________ of the function.

A

derivative

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8
Q

Average rate of change of f(x) on [a,b]

A

f’(x)= (f(b) - f(a))/ b - a

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9
Q

lim x->∞ (1/x)

A

0

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10
Q

What does it mean when a problem states that “f(x) is differentiable?”

A

f’x exists

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11
Q

ln(a*b)=

A

ln(a) + ln(b)

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12
Q

ln(a/b)=

A

ln(a) - ln(b)

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13
Q

lnx^p

A

plnx

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14
Q

What is lim x->c- f(x)

A

The limit of f(x) as x approaches c from the left

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15
Q

What is lim x->c+ f(x)

A

The limit of f(x) as x approaches from the right

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16
Q

What is lim x->c f(x)

A

The limit of f(x) as x approaches from both sides

17
Q

When does the derivative of the function not exist?

A

-When the function is not continuous
-At a corner, cusp, sharp turn
-Vertical tangent line

18
Q

State the relationship between continuity and differentiability?

A

-If f(x) is continuous f(x) may or many not be differentiable
-If f(x) is differentiable f(x) is continuous

19
Q

The Intermediate Value Theorem (IVT):

A

If f(x) is continuous on [a,b], the f(a)<f(c)<f(b) for some c between a and b. (a<c<b)

20
Q

The Mean Value Theorem:

A

If f(x) is continuous and differentiable on [a,b] then f’(c)= (f(b)-f(a))/b-a. For some c between a and b.

21
Q

Equation of a tangent line

A

y-y1=m(x-x1)

22
Q

Different of a square: a^2-b^2=

A

(a+b)(a-b)

23
Q

Definition of derivative

A

f’(x)= lim h->0 f(x+h)-f(x)/h

23
Q

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A
24
Q
A
25
Q
A