Differentiation
What is the notation of the derivative of a function?
f´(x)
What is the notation of a integrated function?
F(x)
What is the slope of the tangent line?
Derivative / IROC
Find the velocity function of a particle with a position modeled by x(t) = 2t3+4t2+14t
v(t) = 6t2+8t+14
What is the limit (as x -> 2) of f(x) = 2x²-4x
0 haha
Differentiate: f(x) = 14x3+2e2x
f'(x) = 42x2 + 4e2x
Integrate f(x) = 6x2 - 4x from (0,2)
8 lol
The average rate of change (AROC) describes the slope of a _____ line.
Secant
Find the slope of the tangent line intersecting point (3,4) if dy/dx = -2x+5y
14 haha
In what cases may L'Hopital's Rule be applied to solve a limit?
If it results in indeterminant form (0/0, infinity/infinity)
Differentiate: f(x)=ln(x2)*ex
f'(x) = (2x*ex)/(x2) + ln(x2)ex
Find the solution for c of the indefinite integral of the function f(x) = 6x2 + 12, given that F(1) = 4
-10
Use a left-handed Riemann Sum to calculate the area under the curve of f(x) = x2 from (0,3)
5 units2
Find the equation of the tangent line given the function f(x) = (x+2)1/2 - 4 , passing through the point (2,-2).
y+2 = (1/4)(x-2)
What is the limit (as x->infinity) of (10x8+14x3-10x)/(3x9+69) ?
0 (horizontal asymptope)
Differentiate (4x)(ln(x))
(4x)(ln(4))(ln(x)) + (4x / x)
Integrate 1 / x2+1
arctan(x) + C
Find the average value of the f(x)=9x2+3x1/2+4 on the interval (0,3)
(2/3)sqrt(27) + 31
Given the circle's diameter is 5 units, at what rate is the area of a circle changing if the radius is increasing at a rate of .5 units/second ?
2.5 pi units2/second
What are the three requirements for continuity?
The limit (as x->a) exists
The limit from the left = limit from the right
The limit (as x->a) = f(a)
Differentiate f(x) = tan(sec(cot(x)))
-csc2(x)sec(cot(x))tan(cot(x))sec2(sec(cot(x)))
Find the indefinite integral of the function f(x) = cos(2x) + 13
(1/2)sin(2x) + 13x + c
Differentiate y = x^x
x^x (1+ln(x))
Find the volume of the solid obtained by rotating the region of the function f(x)=2x+1, bounded by x=4 and y=3, about the line x=-4
126pi
What is the limit (as x->0) of (3x4-4x2)/(x5+12x2) ?
-1/3