Limit process
Definitely fun without calculator
Areas
Let's get triggy with it...
Anything goes
100
lim_(n->oo) sum_(k=1)^n((2k)/n)^4(2/n)=int_0^2?
int_0^2x^4 dx
100
int_0^8(3+x)dx
56
100
Use the intervals indicated in the table to estimate the integral using a left Riemann sum.
int_2^14h'(t)dt
15.3 feet
100
The velocity of an object in feet/sec is given by the function, v(t).
v(t)=5sin(t^2)+cos(2t)-2
Find the total distance traveled by the object during the first 3 seconds.
7.271 feet
100
Trees in a forest are replenished at a rate given by R(t) in acres per week. At time t=0 there are 200 acres of forested land. How many acres of forested land will there be after 4 weeks?
R(t)=t(t+2)
237.333
200
lim_(n->oo) sum_(k=1)^n sqrt(3+k/n)(1/n)=int_3^??
int_3^4 sqrt(x)dx
200
d/(dx)int_1^(x^2)t(t^2+1)dt
x^2((x^2)^2+1)*2xor 2x^7+2x^3
200
int_0^2(x^3+4)dx
Find the trapezoidal approximation for the definite integral using 4 subintervals.
12.25
200
d/(dx)int_1^(x^2)sint^3dt
2 x*sinx^6
200
int_1^3 f(x)dx=-2,int_1^3(f(x)+4)dx=?
6
300
lim_(n->oo) sum_(k=1)^n((32k^2)/n^2+3)(4/n)=int_0^4?
int_0^4(2x^2+3)dx
300
int_0^2x(x^2-1)^3dx
10
300
F(t)=int_1^(t^2) f(x)dx, F'(3)=?
-12
300
int cosx/(sin^3x)dx
-1/(2sin^2x)+C
300
intdx/sqrt(-x^2-4x-3)
sin^-1(x+2)+C
400
lim_(n->oo) sum_(k=1)^n(3(-2+(2k)/n)^2+2(-2+(2k)/n))(2/n)=int_?^??
int_-2^0(3x^2+2x)dx
400
int_1^6 3/x^2dx
5/2 or 2.5
400
The position function x(t) represents the motion of a particle on the x-axis. Given x(5) = 1 and the graph for v(t) below. Find x(10).
2.1
400
int_0^(pi/4) (sec x*tanx)dx
sqrt(2)-1 or 0.414
400
If g(x)=x2 -3x+4 and f(x) = g'(x), then
int_1^3 f(x)dx=
2
500
A tank contains 50 liters of oil at time t=4 hours. Oil is being pumped into the tank at a rate R(t) measured in liters per hour and t is measured in hours. Selected values of R(t) are given in the table. Using a right Riemann sum with three subintervals and data from the table, what is the approximation of the number of liters of oil that are in the tank at time t=15 hours?
114.9 Liters
500
CALCULATOR FRIENDLY(Answer accurate to three decimal places)
Let H(x) be an antiderivative of
(x^3+sinx)/(x^2+2)
If
H(5)=pi,then H(2)=?
-5.867 or -5.866
500
A cup of tea is cooling in a room that has a constant temperature of 70 degrees Fahrenheit. If the initial temperature of the tea, at time t=0, is 200 degrees Fahrenheit and the temperature of the tea changes at the rate R(t) in degrees Fahrenheit per minute, what is the temperature, to the nearest degree, of the tea after 4 minutes?
R(t)=-6.89e^(-0.053t)
175
500
v(t)=5sin(t^2)+cos(2t)-2
The velocity of an object in feet/sec is given by the function, v(t). Find the average rate of change of v(t) over the interval [0, 2]. Identify the units.
-2.719 (ft)/sec^2
500
int(50x^3-55x^2-26x+33)/(10x-7)dx
5/3x^3-x^2-4x+1/2lnabs(10x-7)+C