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AP Calculus Flashcards

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d/dx csc(x)

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Calculus Math

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Mar 1, 2020

Cards (73)

Section 1

(50 cards)

d/dx csc(x)

Front

-csc(x)cot(x)

Back

Which theorem states that average rate of change equals instantaneous rate of change?

Front

Mean Value Theorem

Back

What is the derivative of position?

Front

velocity

Back

If a function is differentiable, then it is also ___________

Front

continuous

Back

What is the tangent line through (2, 5) with f'(2) = 4?

Front

y - 5 = 4(x - 2)

Back

ln ( 1)

Front

0

Back

d/dx cos(x)

Front

-sin(x)

Back

If v(t) > 0 and a(t) < 0 then speed is ____________

Front

decreasing

Back

lim ln (x) = ________ x→0⁺

Front

-∞

Back

What 3 things make a function not differentiable?

Front

discontinuity, sharp edge, vertical tangent line

Back

If f(x) is linear, then f'(x) is

Front

constant

Back

lim eⁿ = ________ n→∞

Front

∞

Back

If v(t) < 0 and a(t) < 0 then speed is _____________

Front

increasing

Back

If f'(x) changes from positive to negative then f(x) has a ___________

Front

relative maximum

Back

d/dx arctan(x)

Front

1/(x²+1)

Back

d/dx xⁿ

Front

nx^(n-1)

Back

d/dx f(x)g(x)

Front

f(x)g'(x) + g(x)f'(x)

Back

∫0 dx

Front

C

Back

d/dx sec(x)

Front

sec(x) tan(x)

Back

If f'(x) = 0 then f(x) has a _________________.

Front

Critical point

Back

d/dx sin(x)

Front

cos(x)

Back

If v(t) > 0 and a(t) > 0 then speed is _____________

Front

increasing

Back

f(x) = x + 3 x ≤ 2 x² x > 2 lim f(x) = ________ x→2⁺

Front

4

Back

d/dx x³

Front

3x²

Back

∫x² dx

Front

1/3x³ + C

Back

A particle is at rest when velocity is ____________

Front

zero

Back

sin(x)/cos(x)

Front

tan(x)

Back

If f(x) is continuous and differentiable and f(a) = f(b), what must happen on the interval [a, b]?

Front

a horizontal tangent line

Back

∫sec(x)tan(x) dx

Front

sec (x) + C

Back

∫1 dx

Front

x + C

Back

If f''(x) < 0 then f(x) is _________________.

Front

Concave down

Back

d/dx x

Front

1

Back

d/dx tan(x)

Front

sec²(x)

Back

sin²(x) + cos²(x)

Front

1

Back

sin⁡〖π/2〗

Front

1

Back

sin⁡〖3π/2〗

Front

-1

Back

What is the derivative of velocity?

Front

acceleration

Back

If f''(x) changes sign then f(x) has an __________________

Front

inflection point

Back

∫x dx

Front

1/2x² + C

Back

d/dx eⁿ

Front

eⁿ

Back

cos (0)

Front

1

Back

lim eⁿ = ________ n→-∞

Front

0

Back

e⁰

Front

1

Back

If f'(x) changes from negative to positive then f(x) has a _____________________

Front

relative minimum

Back

A particle moves right when velocity is ____________

Front

positive

Back

State the conditions for Rolle's Theorem.

Front

continuous, differentiable, f(a)=f(b)

Back

∫csc²(x) dx

Front

-cot(x) + C

Back

lim (4x² + 43)/(9x² - x) x→∞

Front

4/9

Back

d/dx f(g(x))

Front

f'(g(x)) g'(x)

Back

ln(e⁵)

Front

5

Back

Section 2

(23 cards)

What is average rate of change?

Front

slope

Back

What does a definite integral tell us?

Front

area under a curve

Back

State the three conditions for a function to be continuous at a point c.

Front

f(c) exists (there is a point) lim x→c f(x) exists (there is a limit) lim x→c f(x) = f(c) (they agree)

Back

∫sec(x) dx

Front

ln|sec(x) + tan(x)| + C

Back

d/dx f(x)/g(x)

Front

(g(x)f'(x) - f(x)g'(x))/g(x)²

Back

If f''(x) > 0 then f(x) is ____________

Front

Concave up

Back

cos⁡〖π/2〗

Front

0

Back

∫4 dx

Front

4x + C

Back

d/dx cot(x)

Front

-csc²(x)

Back

A particle moves left when velocity is __________

Front

negative

Back

If f'(x) < 0, then f(x) is ___________

Front

decreasing

Back

∫cos(x) dx

Front

sin(x) + C

Back

d/dx 5

Front

0

Back

What does a derivative tell us

Front

slope of a tangent line / instantaneous rate of change

Back

∫tan(x) dx

Front

-ln|cos(x)| + C

Back

∫sin(x) dx

Front

-cos(x) + C

Back

cos ( π)

Front

-1

Back

∫1/x dx

Front

ln |x| + C

Back

∫sec²(x) dx

Front

tan(x) + C

Back

d/dx arcsin(x)

Front

1/√(1-x²)

Back

If f(x) is quadratic, then f'(x) is ___________

Front

linear

Back

sin(0)

Front

0

Back

d/dx ln(x)

Front

1/x

Back