Calculus 1
(arccos x)' - correct answer--1/(√1-x²)
(arccot x)' - correct answer-- 1/(1+x²)
(arcsin x)' - correct answer-1/(√1-x²)
(arctan x)' - correct answer-1/(1+x²)
(log base b (x))' - correct answer-1/xlnb
∫ tanx dx - correct answer-ln|secx| or -ln|cosx|
∫1/(√1-x²) dx - correct answer-sin⁻¹x
∫1/(1+x²) dx - correct answer-tan⁻¹x
∫1/x dx - correct answer-ln|x|
∫b∧x dx - correct answer-(b∧x)/lnb
∫sinhx dx - correct answer-coshx
∫sinx dx - correct answer--cosx
1-tanh²x= - correct answer-sech²x
A function is continuous if... - correct answer-1. f(a) is well defined
2. limf(x) exists
x→a
3. limf(x)=f(a)
x→a
A function is differentiable if... - correct answer-I. f(x) is continuous
1. f(a) is well defined
2. limf(x) exists
x→a
3. limf(x)=f(a)
x→a
II. derivative from L=derivative from R
area of a trapezoid - correct answer-1/2 (a+b)h
c²= - correct answer-a²+b²−2abcosC
, completing the square - correct answer-divide middle by 2 then square it and add to the end
(and subtract)
cos(2x) - correct answer-cos²(x)-sin²(x)
2cos²(x)-1
1-2sin²(x)
cos(a-b) - correct answer-cosacosb+sinasinb
cos(a+b) - correct answer-cosacosb-sinasinb
cosh(x+y) - correct answer-coshx coshy+sinhx sinhy
cosh⁻¹x - correct answer-ln(x+√x²-1) x≥1
cosh²x-sinh²x= - correct answer-1
coshx ' - correct answer-sinhx
cothx' - correct answer--csch²x
cotx prime - correct answer--csc²x
critical number theorem - correct answer-if f has a loc max or min at c, the c is critical
number of f →however, a critical number c may not correspond to a local max or min
csc²(x) - correct answer-1+cot²(x)
cschx ' - correct answer--cschx cothx
cscx prime - correct answer--cotxcscx
d/dx ∫v(x) to u(x) f(t)dt= - correct answer-f(u(x))u'(x)-f(v(x))v'(x)
Definition of the Derivative - correct answer-limh→0 [f(x+h)-f(x)]/h
Extreme Value Theorem - correct answer-if f is CONTINUOUS on a CLOSED interval [a,b]
then f attains a absolute max and min at some number c ∈[a,b]
Finding local/absolute extreme values - correct answer-find critical values- f'(x)=0 or DNE
1st or 2nd derivative test
compare f(a), f(b), and f(critical numbers)
Fundamental Theorem of Calculus part 1 - correct answer-if f is continuous on the closed
interval [a,b] and g(x)=∫a to x f(t)d
FunThmCalc p2 - correct answer-for a continuous function f on [a,b], ∫ a to b f(x)dx=F(b)-F(a)
(arccos x)' - correct answer--1/(√1-x²)
(arccot x)' - correct answer-- 1/(1+x²)
(arcsin x)' - correct answer-1/(√1-x²)
(arctan x)' - correct answer-1/(1+x²)
(log base b (x))' - correct answer-1/xlnb
∫ tanx dx - correct answer-ln|secx| or -ln|cosx|
∫1/(√1-x²) dx - correct answer-sin⁻¹x
∫1/(1+x²) dx - correct answer-tan⁻¹x
∫1/x dx - correct answer-ln|x|
∫b∧x dx - correct answer-(b∧x)/lnb
∫sinhx dx - correct answer-coshx
∫sinx dx - correct answer--cosx
1-tanh²x= - correct answer-sech²x
A function is continuous if... - correct answer-1. f(a) is well defined
2. limf(x) exists
x→a
3. limf(x)=f(a)
x→a
A function is differentiable if... - correct answer-I. f(x) is continuous
1. f(a) is well defined
2. limf(x) exists
x→a
3. limf(x)=f(a)
x→a
II. derivative from L=derivative from R
area of a trapezoid - correct answer-1/2 (a+b)h
c²= - correct answer-a²+b²−2abcosC
, completing the square - correct answer-divide middle by 2 then square it and add to the end
(and subtract)
cos(2x) - correct answer-cos²(x)-sin²(x)
2cos²(x)-1
1-2sin²(x)
cos(a-b) - correct answer-cosacosb+sinasinb
cos(a+b) - correct answer-cosacosb-sinasinb
cosh(x+y) - correct answer-coshx coshy+sinhx sinhy
cosh⁻¹x - correct answer-ln(x+√x²-1) x≥1
cosh²x-sinh²x= - correct answer-1
coshx ' - correct answer-sinhx
cothx' - correct answer--csch²x
cotx prime - correct answer--csc²x
critical number theorem - correct answer-if f has a loc max or min at c, the c is critical
number of f →however, a critical number c may not correspond to a local max or min
csc²(x) - correct answer-1+cot²(x)
cschx ' - correct answer--cschx cothx
cscx prime - correct answer--cotxcscx
d/dx ∫v(x) to u(x) f(t)dt= - correct answer-f(u(x))u'(x)-f(v(x))v'(x)
Definition of the Derivative - correct answer-limh→0 [f(x+h)-f(x)]/h
Extreme Value Theorem - correct answer-if f is CONTINUOUS on a CLOSED interval [a,b]
then f attains a absolute max and min at some number c ∈[a,b]
Finding local/absolute extreme values - correct answer-find critical values- f'(x)=0 or DNE
1st or 2nd derivative test
compare f(a), f(b), and f(critical numbers)
Fundamental Theorem of Calculus part 1 - correct answer-if f is continuous on the closed
interval [a,b] and g(x)=∫a to x f(t)d
FunThmCalc p2 - correct answer-for a continuous function f on [a,b], ∫ a to b f(x)dx=F(b)-F(a)
