Calculus Vocab
See the Derivative
Miscellaneous
C the Integral
Calculus History
Advanced Derivatives!
100
The x-values found when setting
f'(x)=0 or DNE.
What is a critical point.
100
Derivative of: 173pi-3e^2
What is: 0
100
When you integrate a positive function, you find this under the graph of a function and above the x-axis.
What is area.
100
intsinxdx
What is: -cosx + C
100
Calculus is the mathematical study of this one, single word.
What is change.
100
This is the lim_(xrarr2^+)f(x) .
What is 1.
200
This is the value that a function approaches as the input approaches a value.
What is a limit.
200
Derivative of: x3 + 5x2 + x + 1
What is: 3x2 + 10x + 1
200
y-y_0=f'(x_0)(x-x_0)
What is the equation of a tangent line
200
intx+x^2+x^3dx
What is: 1/2x^2+1/3x^3+1/4x^4+C
200
This mathematician contributed mainly to the development of the integral as a sum of many rectangles.
Who is Riemann.
200
***DAILY DOUBLE***
Find dy/dx for x^2+y^3=y-1
What is (2x)/(1-3y^2)
300
If h(x) = f(g(x)) this is used to get h'(x) = f'(g(x))(g'(x))
What is the Chain Rule?
300
Derivative of: ln x
What is: 1/x
300
d/dx and d/dt are notations for this.
What is differentiation?
300
This is the other side of
int_a^bf'(x)dx
What is: f(b)-f(a)
300
f'(x) notation is credited to Fourier. This mathematician gets credit for d/dxf(x) notation.
Who is Leibniz.
300
f(3)=2 and f'(3)=5. What is the equation of the tangent line at x = 3?
y-2=5(x-3)
400
Given that s(t) is the position of the particle, the first of these can solve for 'velocity' and the second for 'acceleration'.
What is a derivative (with respect to time)?
400
Derivative of: tan(x)
What is: sec2(x)
400
lim_(x rarroo)(5x^4-6x^2+1)/(10x^4+12x^3+x)
What is
1/2
400
Looking for the exact answer: int1/xdx
What is: ln |x| + C
400
Gottfried Leibniz and this British scientist are credited with the invention of calculus.
Who is Isaac Newton.
400
d/dx((x^2+1)/(x+3))
(x^2+6x-1)/(x+3)^2
500
This rule/method can be used to find the limit of indeterminate forms like
0/0 and oo/oo
.
What is L'Hospital's Rule?
500
Derivative of: sin(x)+ln(x^2)
What is cos (x) + 2/x ?
500
Other than a hole in the graph, this can cause a discontinuity.
What is a jump or an asymptote.
500
intsqrtxdx
2/3 x^(3/2)+C
500
This foundation of modern calculus was first studied by Cauchy over 100 years after Newton and Liebniz.
What is the Limit.
500
Find and simplify d/dxe^x(2x+3) by factoring out an ex
e^x(2x+5)