# Study sets matching "calculus ab"

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1.) F(c) exists... 2.) limit F(x) as x app…

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

This is a graph of f'(x). Since f'(C) e…

1

f is continuous at x=c if...

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Given f'(x):... Is f continuous @ c?... Is there an inflection point…

1.) F(c) exists... 2.) limit F(x) as x app…

f is continuous at x=c if...

Yes lim+=lim-=f(c)... No, f'(c) doesn't ex…

Given f(x):... Is f continuous @ C... Is f' continuous @ C

Limit Definition of Derivative

Alternate Definition of Derivative

limit as x approaches 0: sinx/x

limit as x approaches 0: ... 1-cosx/x

limit (as h approaches 0)= F(x+h)-F(x)/h

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

1

0

Limit Definition of Derivative

limit (as h approaches 0)= F(x+h)-F(x)/h

Alternate Definition of Derivative

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

Limit Definition of Derivative

Alternate Definition of Derivative

limit as x approaches 0: sinx/x

limit as x approaches 0: ... 1-cosx/x

limit (as h approaches 0)= F(x+h)-F(x)/h

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

1

0

Limit Definition of Derivative

limit (as h approaches 0)= F(x+h)-F(x)/h

Alternate Definition of Derivative

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

What conditions must be to satisfied fo…

If the appropriate conditions are satis…

Limit

Quotient rule?

f(x) is continuous in the interval [a, b] and differentiable i…

There is at least one point c in the interval (a, b) at which…

A limit is the value that a function or sequence "approaches"…

(vu'-uv')/v^2

What conditions must be to satisfied fo…

f(x) is continuous in the interval [a, b] and differentiable i…

If the appropriate conditions are satis…

There is at least one point c in the interval (a, b) at which…

Limit Definition of Derivative

Alternate Definition of Derivative

limit as x approaches 0: sinx/x

limit as x approaches 0: ... 1-cosx/x

limit (as h approaches 0)= F(x+h)-F(x)/h

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

1

0

Limit Definition of Derivative

limit (as h approaches 0)= F(x+h)-F(x)/h

Alternate Definition of Derivative

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

Intermediate Value Theorem

Average Rate of Change

Instantenous Rate of Change

Formal definition of derivative

If f(1)=-4 and f(6)=9, then there must be a x-value between 1…

Slope of secant line between two points, use to estimate insta…

Slope of tangent line at a point, value of derivative at a poi…

limit as h approaches 0 of [f(a+h)-f(a)]/h

Intermediate Value Theorem

If f(1)=-4 and f(6)=9, then there must be a x-value between 1…

Average Rate of Change

Slope of secant line between two points, use to estimate insta…

Limit Definition of Derivative

Alternate Definition of Derivative

limit as x approaches 0: sinx/x

limit as x approaches 0: ... 1-cosx/x

limit (as h approaches 0)= F(x+h)-F(x)/h

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

1

0

Limit Definition of Derivative

limit (as h approaches 0)= F(x+h)-F(x)/h

Alternate Definition of Derivative

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

What conditions must be to satisfied fo…

If the appropriate conditions are satis…

Limit

Quotient rule?

f(x) is continuous in the interval [a, b] and differentiable i…

There is at least one point c in the interval (a, b) at which…

A limit is the value that a function or sequence "approaches"…

(vu'-uv')/v^2

What conditions must be to satisfied fo…

f(x) is continuous in the interval [a, b] and differentiable i…

If the appropriate conditions are satis…

There is at least one point c in the interval (a, b) at which…

Write the notation for the limit of f(x…

Write the notation for the limit of f(x…

State the 3 conditions of continuity of…

List the 3 situations in which a limit…

1. f(c) is defined... 2. The limit of f(x) as x approaches c exis…

1. Unbounded behavior... 2. Differing left/right behavior... 3. Osci…

Write the notation for the limit of f(x…

Write the notation for the limit of f(x…

10

5

6

3/2

Evaluate the limit in Part A given the following information:

Evaluate the limit in Part B given the following information:

Evaluate the limit in Part C given the following information:

Evaluate the limit in Part D given the following information:

10

Evaluate the limit in Part A given the following information:

5

Evaluate the limit in Part B given the following information:

10

5

6

3/2

Evaluate the limit in Part A given the following information:

Evaluate the limit in Part B given the following information:

Evaluate the limit in Part C given the following information:

Evaluate the limit in Part D given the following information:

10

Evaluate the limit in Part A given the following information:

5

Evaluate the limit in Part B given the following information:

Limit Definition of Derivative

Alternate Definition of Derivative

limit as x approaches 0: sinx/x

Basic Derivative

limit (as h approaches 0)= F(x+h)-F(x)/h

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

1

f(x^n)= nX^(n-1)

Limit Definition of Derivative

limit (as h approaches 0)= F(x+h)-F(x)/h

Alternate Definition of Derivative

limit (as x approaches a number c)=... f(x)-f(c)/x-c x≠c

Limit Definition of Derivative

limit as x approaches 0: sinx/x

limit as x approaches 0: ... 1-cosx/x

Continuity Rule

limit (as h approaches 0)= F(x+h)-F(x)/h

1

0

If the limit exists (aka left limit and right limit are equal)…

Limit Definition of Derivative

limit (as h approaches 0)= F(x+h)-F(x)/h

limit as x approaches 0: sinx/x

1

10

5

6

3/2

Evaluate the limit in Part A given the following information:

Evaluate the limit in Part B given the following information:

Evaluate the limit in Part C given the following information:

Evaluate the limit in Part D given the following information:

10

Evaluate the limit in Part A given the following information:

5

Evaluate the limit in Part B given the following information: