問題一覧
1
What is the most proved theorem in mathematics and how many proofs it has?
Pythagorean theorem with more than 370 proofs
2
Where did calculus derive from
derive from latin word calx which means stone and greek work chalis which means limestone
3
He published his early work of calculus on ______ and what is his name?
he published his early works of calculus on 1684 and his name is Gottfried Wilhelm Von Leibniz
4
English astronomer, physicist, and mathematician who made his early study of calculus but did not publish until?
1704
5
Founder of todays calculus
Isaac Newton and Gottfried Wilhelm Von Leibniz
6
Areas of calculus
differential calculus, integral calculus, differential calculus, calculus of variations
7
Branch of mathematics which deals with limits ad derivatives
differential calculus
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What is this branch of dc to Let f be a function that is define on an open interval containing
limits
9
What is derivatives?
function expresses the rate of change with respect to an independent variable
10
A straight lune that touches the curve at a given point
tangent line
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A point on the graph where the derivative is zero or undefined
critical point
12
A point on the curve where the concavity changes meaning the second derivative changes sign
infliction point
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Describes the direction of the curvature of a graph
concavity
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A technique used to differentiate equations where y is not implicitly solve for x
implicit differentiation
15
Integral of sin u du
-cos u du +c
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Integral of cos u du
sin u du +c
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Integral of tan u du
ln sec u +c
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Integral of cot u du
ln sin u +c
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Integral of sec u du
ln (sec u + tan u) +c
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Integral of du
u+c
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Integral of u^n du
u^n+1/n+1 +c
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Integral of du/u
ln u +c
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Integral of e^u du
e^u +c
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Integral of ln u du
u ln u - u +c
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Derivative of constant
0
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Derivative of d(u^n)
nu^n-1 du
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Derivative of d(u+v)
du+dv
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Derivative of sin u
cos u du
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Derivative of cot u
csc² u du
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Derivative of sec u
sec u tan u du
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Derivative of csc u
-csc u cot u du
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Derivative of log a^u
log e^du/u
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Derivative of tan u du
sec² u du
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Derivative of e^u
e^u du
35
Derivative of ln u
du/u