Limits
lim_(x->3)(x^2-9)/(x-3)
6
f(x)=(2x+3)^3 . Find f'(x)
f'(x)=6(2x+3)^2
Who walked on the moon on the Apollo 11 mission?
Neil Armstrong and Buzz Aldrin
What is the name of Ms. Cordano's Pet?
Apollo
lim_(x->7)(2x^2-8x-42)/(x-7)
20
f(x)=sin^3(x), f'(x)=?
3sin^2(x)cos(x)
Who was the first US President to live in the White House?
John Adams
What is Ms. Cordano's favorite branch of mathematics?
Geometry
lim_(x->4)(2x^3-128)/(5x-20)
96/5
xy+e^(y)+3x=15, dy/dx=?
dy/dx=(-3-y)/(x+e^y)
Air is being pumped into a spherical balloon at a rate of 5 (cm^3)/min . Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm. (The volume of a sphere is V=4/3pir^3 ).
(dr)/dt=1/(80pi)
lim_(x->oo)(e^(4x))/(x^2+1)
oo
f(x)=sin^2(x) . What is the third derivative of f(x)? FULLY SIMPLIFY (but don't use trig identities)
f'''(x)=-8sinxcosx
You are standing ten miles away from the launch pad of a rocket. The rocket lifts off with velocity of 20 miles per minute. At what rate is the angle of elevation from you to the rocket changing when the rocket is 3 miles in the air? (Answer in radians).
1.83486 (rad)/min
log_3(x)+e^(2y)+cot^-1(y)=xe^(y^2), dy/dx=? You can keep complex fractions in this answer.
dy/dx=(e^(y^2)-1/(xln3))/(2e^(2y)-1/(1+y^2)-2xye^(y^2)
A 15 foot ladder is resting against a wall. The bottom is initially 10 ft away from the wall, and is being pushed towards the wall at a rate of 1/4 (ft)/sec . How fast is the top of the ladder moving 12 seconds after we start pushing?
7/(4sqrt(176)) or 0.1319 (ft)/sec