Derivatives
x2
2x
What is an intended y-value?
It is the value that the limit approaches.
What is an integral?
The area under the curve.
How do you take the derivative of a function?
Math 8
What is the formula for the product rule?
y'=f'(x)*g(x)+f(x)*g'(x)
sinx
cosx
How do you write the limit is approaching a number from the left?
limx→a-
What is the difference between the washer method and the disk method?
The disk method does not include empty space(r2), while the washer method does(R2-r2).
How do you find the definite integral of a function?
Math 9
What is the formula for the quotient rule using f(x)/g(x)?
y'=g(x)*f'(x)-f(x)*g'(x)/(g(x))2
tanx
sec2x
What is l'hopital's rules?
limx→a f(x)/g(x)=limx→a f'(x)/g'(x)
When is u-substitution used?
When taking the derivative of the integrated. If the chain rule is needed then the antiderivative will need u-substitution.
How do you find the point in which two functions intersect?
2nd Calc 5
What is the formula for the chain rule?
tan-1x
1/x+1
What is it called when limx→∞ or limx→-∞
End behavior or a Horizontal Asymptote
What is the fundamental theorem of calculus?
d/dx ∫ab f(t)dt=f(x)
How do you find where a function crosses the x-axis?
2nd Calc 2
What is the formula for the power rule?
f'(x)=nxn-1
cos-1x
-1/sqrt(1-x2)
What are the conditions required for a function to be continuous?
The function must be defined at that point. The limit must exist at that point. The limit and the function must have equal values at that point.
What is the average value of a function on an interval?
1/b-a ∫ab f(x)dx
How do you input a function from y= into the calculator
Alpha calc
What is the formula for the sum rule?
[f(x)+g(x)]=f'(x)+g'(x)