The velocity of a particle moving on a line at time t is v=5t +6t .How many meters did the particle travel from t=1 to t=8?
282
100
Integrate
∫(5x +4)^5 dx
(1/30)(5x+4)^6+C
100
Differentiation the function
f(x)=(3x+1)^2
6(3x+1)
200
The limit as x approaches 3
(x/(x^2 -2x-3))
∞
200
Find the derivative of the function
f(x)=(x^2)/ln(2)
f'(x)=2x/ln(2)
200
On the moon, an object is dropped straight down into a crater 150 m deep. The height of the object from the bottom of the crater, as it falls, is given by:
h(t)=−0.8t^2+150.
What is the acceleration due to gravity on the moon?
−0.16m/s^2
200
Integrate
∫t^2(t^3 +4)^(−1/2) dt
(2/3)(t^3 +4)^(1/2)+C
200
The limit as x approaches -5
(y^2)/(5-y)
5/2
300
The limit as ∆x approaches 0
((x-∆x)^3- x^3) /∆x
3x^2
300
Find the derivative of the function
f(x)=(x^3)/(1−x^2)
(3x^2−x^4)/(1−2x^2+x^4)
300
A bullet is fired straight upward at a speed of 900 m/s. The equation relating its height as a function of time is
h(t)=−4.9t^2 +900t + 2.4 .
How long does it take to hit the ground?
h(t)=0 when t=183.7 seconds
300
Integrate
∫(sin^10 x)(cosx) dx
(1/11)sin^11 x+C
300
HIDDEN EASY QUESTION!!
What is the quadratic formula?
x= (-b (+ or -) √b^2 -4ac) / 2a
400
The limit as x approaches π/2
(tanx)
The limit does not exist!
400
Find the derivative of the function
f(x)=t/(2t−1)^2
f'(x)=−(2t+1)/(2t−1)^3
400
The position of the particle traveling along a straight line is
x(t)=(−t^3)-(9t^2)+15t+3).
On the interval t=0 to t=10, when is the particle farthest to the left?
t=5
400
Integrate
∫sinx /(cosx)^5 dx
(1/4)(cosx)^(−4)+C
400
Integrate
∫(x^3-2x^2)((1/x)-5) dx
(-5/4)x^4 + (11/3)x^3 - x^2 +C
500
The limit as ∆x approaches 0
(5(x+∆x)^2 -5x^2) /∆x
10x
500
Find the derivative of the function
f(x)=√xe^x
f'(x)=(e^x)/(2√x +√xe^x)
500
When two particles start at the origin with velocities
v(t)=4cost and v(t)=4sint , how many times in the interval [0, 2π] will their speeds be equal?