The limit used to define the slope of a tangent line is also used to define one of the two fundamental operations of calculus
What is Derivative
100
when points meet from the left and from the right at a certain x value are equal
What is a limit
100
anti-derivatives
What is integration
100
pi*integral of f(x) from (a,b) with respect to x
What is volume
100
2+2
What is fish
200
((sec^2 u)*u prime) is the derivative.
What is the derivative of tan (u)
200
the limit as x^2 +16x approaches x=6
What is 132
200
integral of x^2 +3x + 6 +0.5
What is (1/3)x^3 +(3/2)x^2 + 6.5x
200
f(x)=x +1, at (0,5)
Volume about the x-axis?
What is 225.147
200
Calculus of a Single Variable author(s)
Who is Ron Larson and Bruce Edwards
300
limit of (f(x+h)-f(x))/h
What is the limit process
300
the limit of sin (1/x) approaches x=0
What is Does Not Exist
300
indefinite integral of 6x^3 + (x)^(1/2)
What is (3/2)*x^4 +2*x^(3/2) + C
300
V= integral of ((3^(1/2))/4)*(A(x))^2 dx from (a,b)
What is Volume with Equilateral triangle cross sections
300
derivative of arccot(x)
What is 1/(-csc^2 (y))
400
f(x)=(4x^4 +96x^3+2)/(x^2 + 45)
What is ((x^2 +45)*(16x^3 +288x^2)-(4x^4 +96x^3 +2)*(2x))/(x^2 +45)^2
400
f(x) approaches a different number from the right side of c than it approaches from the left side.
f(x) increases or decreases without bound as x approaches c.
f(x) oscillates between two fixed values as x approaches c.
What is behaviors of nonexistence of limits
400
Integral of (x+1)/ (x^(1/2))
What is (2/3)*(x^(1/2))*(x+3) + C
400
V=(1/3)*h*B
A(y)=(b^1)^2
V= integral of A(y)dy from (0,h)
What is Volume of pyramids
400
g prime of x is equal to 1 over the f prime of g of x
g^1(x)= 1/(f^1g(x))), where f prime of g of x cannot equal zero
(f^1g(x))) != 0
What is Derivative of an inverse Function
500
f(x)=(8x+5)^3
f^1(x)=
f^2(x)=?
What is 384(8x+5)
500
the limit of ((2+x)^(1/2) - (2)^(1/2))/x as x approaches zero
What is 1/(2*sqrtroot2)
500
Somewhere "between" the inscribed and circumscribed rectangles, there is a rectangle whose area is precisely equal to the area of the region under the curve.
What is Mean Value Theorem for Integrals
500
The volume is the integrated at (a,b) in where the functions are R^2-r^2 and the integral is multiplied by pi
What is the Washer Method
500
integral of u^n * du = (u^(n+1))/(n + 1) +C, n cannot = -1.