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∫kf(x)dx

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Date created

Mar 1, 2020

Cards (68)

Section 1

(50 cards)

∫kf(x)dx

Front

k∫f(x)dx

Back

d/dx[tanu]=

Front

d/dx[tanu]= (sec²u)u'

Back

∫csc(x)cot(x)dx

Front

-csc(x) + C

Back

A critical number occurs when:

Front

f'(x)=0 or is undefined and f(x) is changing from increasing to decreasing or vice versa.

Back

Average Rate of Change

Front

[f(b)-f(a)]/(b-a)

Back

d/dx [cosu]

Front

(-sinu)(u')

Back

∫csc²(x)dx

Front

-cot(x) + C

Back

∫csc(u)du

Front

-ln|csc(u)+cot(u)| + C

Back

∫(1/u)du

Front

ln|u| + C

Back

d/dx [c]

Front

0

Back

d/dx[e∧u]

Front

(e^u)u'

Back

∫tan(u)du

Front

-ln|cos(u)| + C

Back

lim(x→ ±∞)(ƒ(x))= If the degree of the numerator is > the degree of the denominator

Front

Does not exist

Back

The line y=L is a horizontal asymptote of the graph of ƒ if:

Front

lim(x→ ±∞)(ƒ(x))= L

Back

d/dx[ln(u)]=

Front

u'/u

Back

∫kdx

Front

kx+C

Back

d/dx[lnu]

Front

u'/u

Back

Quotient Rule d/dx[f(x)/g(x)]=

Front

d/dx[f(x)/g(x)]= [g(x)f'(x)-f(x)g'(x)]/[g(x)]²

Back

lim(x→ ±∞)(ƒ(x))= If the degree of the numerator is = the degree of the denominator

Front

The ratio of the leading coefficients

Back

d/dx[secu]=

Front

d/dx[secu]= (secu·tanu)u'

Back

d/dx[cscu]=

Front

d/dx[cscu]= -(cscu·cotu)u'

Back

Limit definition of a derivative

Front

ƒ'(x)= lim(∆x→0) [f(x+∆x)-f(x)]/ (∆x)

Back

A function is continuous if the following 3 conditions are met:

Front

1. ƒ(c) is defined 2. lim(x→c)(ƒ(x)) exists 3. ƒ(c) = lim(x→c)(ƒ(x))

Back

∫cot(u)du

Front

ln|sin(u)| + C

Back

lim(x→ ±∞)(ƒ(x))= If the degree of the numerator is < the degree of the denominator

Front

0

Back

lim(x→0)[(sinx)/x]=

Front

1

Back

∫0dx

Front

C

Back

lim(x→0)[(1-cosx)/x]=

Front

0

Back

∫sec²(x)dx

Front

tan(x) + C

Back

d/dx [sinu]

Front

(cosu)(u')

Back

When does the derivative of f(x) not exist?

Front

f(x) is undefined, where f(x) has a sharp turn, where f(x) has a vertical tangent line

Back

lim(x→c)(x)=

Front

c

Back

Product Rule: d/dx[f(x)g(x)]=

Front

d/dx[f(x)g(x)]= f(x)g'(x)+g(x)f'(x)

Back

If f and g are inverse functions, g'(x)=

Front

1/ƒ'(g(x))

Back

∫sin(x)dx

Front

-cos(x) + C

Back

If s(t)= Position, then s'(t) = s''(t)=

Front

s'(t)= velocity s''(t) = acceleration

Back

∫sec(x)tan(x)dx

Front

sec(x) + C

Back

d/dx[cotu]=

Front

d/dx[cotu]= -(csc²u)u'

Back

lim(x→c)(b)=

Front

b

Back

d/dx [uⁿ]

Front

nuⁿ⁻¹u'

Back

lim(x→c)(x^n)=

Front

c^n

Back

Average value of f on an interval (a,b)

Front

1/(b-a)∫f(x)dx [NOTE: limits of integration are from a to b]

Back

If ƒ(x) approaches ±∞ as x approaches c from the right or left, then x=c is a ________

Front

Vertical Asymptote

Back

Instantaneous Rate of Change at x=c of f(x)

Front

=f'(c)

Back

∫[f(x)±g(x)]dx

Front

∫f(x)dx ± ∫g(x)dx

Back

A point of inflection occurs when:

Front

f''(x)=0 or is undefined and f(x) is changing from concave upward to concave downward or vice versa.

Back

∫xⁿdx

Front

[x∧(n+1)]/(n+1) + C

Back

∫cos(x)dx

Front

sin(x) + C

Back

∫sec(u)du

Front

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

Back

When does a limit fail to exist?

Front

1. The left handed limit does not equal the right handed limit 2. Unbounded behavior 3. Oscillating

Back

Section 2

(18 cards)

d/dx[arcsinu]=

Front

u'/√(1-u²)

Back

d/dx[arcsecu]=

Front

u'/(|u|√(u²-1))

Back

∫cscucotudu=

Front

-cscu + C

Back

d/dx[arccotu]=

Front

-u'/(1+u²)

Back

∫du/(u√(u²-a²))

Front

(1/a)arcsec(|u|/a) + C

Back

∫e^u du

Front

e^u + C

Back

∫a^x dx

Front

(a^x)/(lna) + C

Back

d/dx[a^u]

Front

(lna)(a^u)(u')

Back

d/dx[arccosu]=

Front

-u'/√(1-u²)

Back

d/dx[loga u]

Front

u'/[(lna)(u)]

Back

d/dx[secu]=

Front

(secutanu)u'

Back

d/dx[cscu]=

Front

-(cscucotu)u'

Back

d/dx[arccscu]=

Front

-u'/(|u|√(u²-1))

Back

∫du/(a²+u²)

Front

(1/a)arctan(u/a) + C

Back

∫du/√(a²-u²)=

Front

arcsin(u/a) + C

Back

d/dx[|u|]=

Front

(u×u')/|u|

Back

d/dx[arctanu]=

Front

u'/(1+u²)

Back

d/dx[cotu]=

Front

-(csc²u)u'

Back