LIMITTS
limit of x approaching -4
(2x^2+3x-2)
18
What is the derivative of f(x)= sin (x)
Cos (x)
What is f'(x) = [g(x) × f'(x) + f(x) × g'(x)]
Product rule
acceleration
is the rate of change of the velocity, that is, the derivative of velocity.
what is the anti derivative of ƒ(x) = 2x
F(x) = x^2
limit of x approaching 10
x^2-5x-50/x-10
15
Find the derivative of f(x)= 4x^4 + 2x^3 - 4x^2+5x - 81
f'(x)= 16^3 + 6x^2 - 8x + 5
What is the derivative of f(x) = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]2
Quotation Rule
concavity
the upward r downward curve of the graph of a function
what is the anti derivative of g(x) = cos x
sin (x)
limit of x approaching 0
1/x+1 - 1/x
-1
Find the second derivative of f(x)= sin (x) + 3x^5
f'' (x) = -sin (x) + 60x^3
What rule is d/dx ( f(g(x) ) = f' (g(x)) · g' (x)?
Chain Rule
critical point
if f'(c)=0 or f'(c) is undefined, we say that c is the critical point of f.
What is the anti derivative of h(x) = 2x + cos x
H(x) = x^2 + sin x
limit of x approaching 0
sin(7x)/11x
TRUE OR FALSE: If the derivative of a function is increasing, it concaves down.
FALSE
What is d/dx (sin 2x)?
2 cos 2x
definite integral
a primary operation of calculus; the area between the curve and the x-axis over a given interval is a definite integral.
What is the integral of (x^2 - 2x + 5) dx?
= x^3/3 - x^2 + 5x + C.
limit of x approaching 0
sin^2(3x)/ sin^2(5x)
9/25
TRUE OR FALSE: You can only derive an equation twice
FALSE
TRUE OR FALSE: dy/dx = dy/du · du/dx is another way to solve chain rule
TRUE
extreme value theorem (evt)
if f is a continuous function over a finite, closed interval, then f has an absolute maximum and an absolute minimum.
TRUE OR FALSE : If such a function F exists, it is called an antiderivative of ƒ.
TRUE