Limits
lim_(x\to3) (x^2-9)/(x-3)
What is 6?
d/dx(5x^4+3x)
What is
20x^3+3
When calculating R_N or L_N of f(x) on [a,b] , this is how we find \Delta x
What is
\Delta x=(b-a)/N
Integrate sin(t) with respect to t from 0 to 2pi
What is 0?
What is the first fundamental theorem of calculus?
\int_a^b f(x) dx = F(b)-F(a)
where
F(x)
is an antiderivative of
f(x)
\lim_(x\to2) (x^2-4)/(4x^2+5x-6)
What is 0?
d/dx(1/sqrtx^5)
What is
-5/2x^(-7/2)
Use right end points to approximate the area using n=8 on the interval [0,4] for the function
g(x)=2x^2+5
What is 71?
int_2^3(x^3-4x^2+5x-10)dx
What is -329/50?
What does the first derivative test find/tell us about the original function?
Where f(x) is increasing/decreasing and if f(x) has any relative extrema
\lim_(x\to-3) (x^2-5x-24)/(x+3)
What is -11?
d/dx(x^3/cos x)
What is
(3x^2 cosx+x^3sin(x))/cos^2(x)
What doe Riemann sums find?
What is the approximate area under the curve?
int(5x^3+(3^(x))^4)dx
What is
5/4x^4 +((3^(x))^4)/(4ln(3))+C
?
What does the 2nd derivative find?
Whether f(x) is concave up/down and whether f(x) has points of inflection
Whether a critical number is the location of a rel max/min
lim_(x\to0) sinx/x
What is 1?
d/dt(tan(ln(t)))
What is
sec^2(ln(t))/t
The integral of some function f(x) over the interval [2,b] is estimated below using left endpoints and 4 equal subdivisions. What is f(x) and what is b?
3[sqrt2+1]+3[sqrt5+1]+3[sqrt8+1]+3[sqrt11+1]
What is
f(x)=\sqrtx
and
b=14
?
int sec^2(sqrt x)/sqrtx dx
What is
2tan(sqrtx)+C
?
How fast does the radius of a balloon change if it is filled with air at a rate of 10 cubic cm per second?
What is
5/(2pi r^2) (cm)/(sec)
What is the limit definition of the derivative of
f(x)?
lim_(x\to a) (f(x)-f(x))/(x-a)
lim_(h\to 0) (f(x+h)-f(x))/h
Find dy/dx given
y^3-x^2=x+y
What is
dy/dx=(1+2x)/(3y^2-1)
Give an example of a function and an interval for which Right end point approximation would be an UNDER estimate.
*Answers will vary*
Examples
f(x)=x^2, [-1,0]
g(x)=sin(x), [n/2,n]
int (2ln(x^2))/(3x) dx
What is
An open top box is to be made by cutting small congruent squares from the corners of a 12X12 square inch sheet of metal. How large should the squares be so the box will hold as much as possible?
What is
2\text( inches by ) 2\text( inches)