Limits
The solution to limx-->0(ln(x))
What is -∞?
The solution to ∫sin(x)dx
What is -cos(x)+C?
logab=logcb/logca
What is the change of base formula?
The solution to dy/dx(1/x)
What is -1/x2?
The solution to dy/dx=x/y
What is y=√(x2+c1) , y=-√(x2+c1)?
The solution to limx-->0(sin(x)/x))
What is 1?
The solution to ∫(1/x2)dx
What is -(1/x)+C
The Steps for Logarithmic Differentiation
1) Simplify after taking "ln" of both sides
2) Differentiate each side
3) Isolate f'(x)
The solution to dy/dx(x2+9x+20)
What is 2x+9?
The solution to dy/dx=sin(x+y)
What is y=2tan-1(-2-x-c1/x+c1)+2πn-x
The solution to limx-->4((√x)-8/x-7))
What is 2?
The solution to 4∫4π0(4/e-xdx)
What is 4(e4π-1)?
The theorem that states that the derivative would have a certain value at some point.
What is Mean Value Theorem (MVT)?
The solution to dy/dx(x2sin(x))
What is 2xsin(x)+cos(x)x2?
The solution to dy/dx=18/x4
What is y=-(6/x3)+c1
The solution to limx-->1(sin(π(x2-5)/3))
What is √3/2?
The solution to ∫π0(x2+8+15)dx
What is (π3/3)+4π2+15π?
If f is an integrable function and g(x) equals the integral of f(x)dx, then the integral of f(x)dx from a to b equals g(b)-g(a)
What is the Fundamental Theorem of Calculus?
The solution to dy/dx(4x2+12x+36/3x-2)
What is 12x2-16x-132/(3x-2)2?
The solution to x3/(x2+4x+4)
What is y=-(x3/x+2)+3(0.5x2-2x+4ln(x+2)-6)+c1?
The solution to limx-->2((3x4+7x3)*(2x4+4x3)/(x+5)*(x+4))
What is 3328/21 or 158.48?
The solution to ∫50(√(x2+25)dx)
What is 25*(√(2)+ln(1+√2))/2?
The Derivatives of the 6 Trigonometric Functions
What are sin(x)'=cos(x), cos(x)'=-sin(x), tan(x)'=sec2(x), csc(x)'=-csc(x)cot(x), sec(x)'=sec(x)tan(x), and cot(x)'=-csc2(x)?
The solution to dy/dx(tan(x)-8/csc(x))
What is sec2(x)+cot(x)(tan(x)-8)/csc(x)?
The solution to dy/dx=351sin(x)/cot(x)
What is y=351(-sin(x)+ln(tan(x)+sec(x)))+c1?