2023-12-13T17:29:44+03:00[Europe/Moscow] en true <p>Rational function definition</p>, <p>True or false: cos(x) is an even function</p>, <p>A function is left continuous at a point c if _______</p>, <p>A function is continuous at a point c if ________</p>, <p>Formal definition for right and left continuous functions</p>, <p>First principles derivative formula</p>, <p>Is this concave up or down?</p>, <p>Convex is also called concave _______</p>, <p>Concave is also called concave __________</p>, <p>Is this concave up or down?</p>, <p>Is this concave up or down?</p>, <p>Notes limit notation</p>, <p>is -x^2 bounded above or below?</p>, <p>An oblique asymptote is formed when the degree of the numerator polynomial is ____________ than the degree of the denominator polynomial</p>, <p>Derivative of |x|</p>, <p>Notes improper integrals</p>, <p>L'hopital's rule is only applicable with the indeterminate forms _______ and _______</p>, <p>Is f(x)=x^3 increasing at x=0?</p>, <p>If the second derivative is negative, at that point is the function concave up or down?</p>, <p>Min-max theorem: a __________ function on a ________, __________ domain reaches an absolute minimum and maximum</p>, <p>Square brackets mean the endpoint is _________, while round brackets mean it is ___________</p>, <p>Average value of a function on [a, b] formula</p>, <p>Sequences - convergence definition</p>, <p>Can a sequence have a vertical asymptote?</p>, <p>Is the convergence/divergence of a sequence affected by addition, subtraction, multiplication or division (using a constant)?</p>, <p>Squeeze theorem definition</p>, <p>Positive/negative sequence definition</p>, <p>Geometric series sum to infinity formula</p>, <p>If the integral of a function converges, does the series denoted by that function converge as well?</p>, <p>What is the p-series</p>, <p>1/n is called the _______ series</p>, <p>If the integral of a function diverges, does the series denoted by that function diverge as well?</p>, <p>What is the comparison test?</p>, <p>The comparison, limit comparison and ratio tests only work for _______ series.</p>, <p>What is the limit comparison test?</p>, <p>If after applying the limit comparison test L=3 and Σbₙ converges, can you conclude anything about Σaₙ?</p>, <p>If after applying the limit comparison test L=∞ and Σbₙ converges, can you conclude anything about Σaₙ?</p>, <p>If after applying the limit comparison test L=∞ and Σbₙ diverges, can you conclude anything about Σaₙ?</p>, <p>If after applying the limit comparison test L=0 and Σbₙ diverges, can you conclude anything about Σaₙ?</p>, <p>What is the ratio test?</p>, <p>If after applying the ratio test p=1, what can be concluded (if anything)?</p>, <p>If after applying the ratio test p&gt;1, what can be concluded (if anything)?</p>, <p>What is absolute convergence?</p>, <p>A series that is convergent but not absolutely convergent is called ________ convergent</p>, <p>What is the alternating series test?</p>, <p>For the alternating series test to be applicable, aₙ as n-&gt;∞ must tend to _.</p>, <p>Not in lectures - What is the integrating factor formula?</p>, <p>Is the differential equation y' + sin(y) = x linear?</p>, <p>Is the differential equation y' + ysin(x) = x^2 linear?</p>, <p>What does ODE stand for?</p>, <p>What is order? (differential equations)</p>, <p>What is degree? (differential equations)</p>, <p>Symbol used instead of 'd' in partial derivatives</p> flashcards
Calculus Period 2

Calculus Period 2

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  • Rational function definition

    A fraction where the numerator and denominator are polynomial functions

  • True or false: cos(x) is an even function

    True

  • A function is left continuous at a point c if _______

    While approaching c from the left, the function is continuous

  • A function is continuous at a point c if ________

    It is continuous while approaching c from the left and right; it is right continuous and left continuous

  • Formal definition for right and left continuous functions

  • First principles derivative formula

  • Is this concave up or down?

    Is this concave up or down?

    Up

  • Convex is also called concave _______

    Up

  • Concave is also called concave __________

    Down

  • Is this concave up or down?

    Is this concave up or down?

    Down

  • Is this concave up or down?

    Is this concave up or down?

    Up

  • Notes limit notation

  • is -x^2 bounded above or below?

    Above

  • An oblique asymptote is formed when the degree of the numerator polynomial is ____________ than the degree of the denominator polynomial

    1 higher

  • Derivative of |x|

    x / |x|

  • Notes improper integrals

  • L'hopital's rule is only applicable with the indeterminate forms _______ and _______

    [0 / 0], [∞ / ∞]

  • Is f(x)=x^3 increasing at x=0?

    Yes, despite the derivative being 0

  • If the second derivative is negative, at that point is the function concave up or down?

    Down

  • Min-max theorem: a __________ function on a ________, __________ domain reaches an absolute minimum and maximum

    Continuous, closed, bounded

  • Square brackets mean the endpoint is _________, while round brackets mean it is ___________

    included, excluded

  • Average value of a function on [a, b] formula

  • Sequences - convergence definition

    After an index N, all terms aₙ are within a distance ε from the limit L

  • Can a sequence have a vertical asymptote?

    No

  • Is the convergence/divergence of a sequence affected by addition, subtraction, multiplication or division (using a constant)?

    No

  • Squeeze theorem definition

  • Positive/negative sequence definition

    All terms are positive/negative

  • Geometric series sum to infinity formula

  • If the integral of a function converges, does the series denoted by that function converge as well?

    Yes

  • What is the p-series

  • 1/n is called the _______ series

    Harmonic

  • If the integral of a function diverges, does the series denoted by that function diverge as well?

    Yes

  • What is the comparison test?

  • The comparison, limit comparison and ratio tests only work for _______ series.

    Positive

  • What is the limit comparison test?

  • If after applying the limit comparison test L=3 and Σbₙ converges, can you conclude anything about Σaₙ?

    Yes, that Σaₙ also converges.

  • If after applying the limit comparison test L=∞ and Σbₙ converges, can you conclude anything about Σaₙ?

    No

  • If after applying the limit comparison test L=∞ and Σbₙ diverges, can you conclude anything about Σaₙ?

    Yes, that Σaₙ also diverges.

  • If after applying the limit comparison test L=0 and Σbₙ diverges, can you conclude anything about Σaₙ?

    No

  • What is the ratio test?

  • If after applying the ratio test p=1, what can be concluded (if anything)?

    There is no conclusion

  • If after applying the ratio test p>1, what can be concluded (if anything)?

    Σaₙ diverges, and aₙ -> ∞

  • What is absolute convergence?

  • A series that is convergent but not absolutely convergent is called ________ convergent

    Conditionally

  • What is the alternating series test?

  • For the alternating series test to be applicable, aₙ as n->∞ must tend to _.

    0

  • Not in lectures - What is the integrating factor formula?

  • Is the differential equation y' + sin(y) = x linear?

    No

  • Is the differential equation y' + ysin(x) = x^2 linear?

    Yes

  • What does ODE stand for?

    Ordinary differential equation

  • What is order? (differential equations)

    The highest derivative that a differential equation contains. Eg. in y'' + xy' + y = x, the order is 2 because of y''.

  • What is degree? (differential equations)

    The power to which the highest order derivative is raised. Eg. in (y'')^3 + y'x + 2xy = 0, the degree is 3, since the highest order derivative y'' is raised to the 3rd power.

  • Symbol used instead of 'd' in partial derivatives

    ∂