# 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

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…

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

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:

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

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

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: