Derivatives
Anti-derivatives
Riemann Sums
Limits
Tangent Line
100
cos(x)
-sin(x)
100
-sin(x)
Cos(x)+C
100
Use a Right Riemann Sum with 4 equal subintervals to approximate the total number of cookies over the interval (1,4)
63 cookies
100
Find the limit as x approaches -3 of (x2+4x+3)/(x2-3)
0
100
Find the equation of the line tangent to x2+1 at x=2
y=4x-3
200
3x5-2x2-7
15x4-4x
200
X5-X2
(1/6)X6-(1/3)X3+C
200
Use a Left Riemann Sum with 4 subintervals to approximate y over the interval (-2,2)
-10
200
Find the limit as x approaches 0 of (1-cos(x))/x2
1/2
200
Find the equation of the line tangent to x(1/2) at x=9
y=(1/6)x+(3/2)
300
(3x2-5x+1)2
4(6x-5)(3x2-5x+1)3
300
3x4-2x(1/2)+5x-2
(3/5)x5-(4/3)x(3/2)-5x-1+C
300
Use a trapezoidal sum to find the approximate value over the interval (-3,2)
-12.5
300
Find the limit as x approaches 2 of (x3-8)/(x-2)
12
300
Find the equation of the line tangent to ln(x) at x=1
y=x-1
400
4x^(-1/2)
-2/(x(3/2))
400
sin(3x)
-(1/3)cos(3x)+C
400
Use a right Riemann sum to approximate y over the interval (1,10)
92
400
Find the limit as x approaches infinity of (5x2-3x+1)/(2x2+7)
5/2
400
Find the equation of the line tangent to ex at x=1
y=e(x-1)+e
500
((x2+1)1/2) /( x3+2)
(-2x4-3x2+2x)/((x2+1)1/2)(x3+2)2)
500
X2ln(x)
(X3/3)ln(x)-(X3/9) + C
500
9.5
500
Find the limit as x approaches 0 of (ex-1-x)/(x2)
1/2
500
Find the equation of the line tangent to sin(x) at x=pi/6
y-(1/2)=(31/2/2)(x-(pi/6))