Algebra and Limits
Do limits have to be continuous or differentiable?
continuous
How do you solve an integral?
Take the antiderivative
Find the derivative y = cos(e^pix)
dy/dx = -sin(e^pix) x (e^pix) x pi
Find the area below f(x) = x^3-10x^2+18x+3 and above g(x) = x^2+7x-10 over the interval
1≤x≤2
7.583
Limit as x approaches 2 (8-3x+12x^(2))
evaluate the limits
f(x)= {x+13
f(x)= {√(x+6) -7
limit as x approaching 10 from the left and from the right
limit as x approaches 10
limit as x approaching 10 from the left = 23
limit as x approaches 10 from the right = -3
limit as x approaches 10= DNE
If this graph shows the relationship between water pressure and time, how much water is there after 10 hours?
look at picture
4 gallons
This is the graph of the DERIVATIVE of a function, using this determine the increasing intervals of the function
look at picture
(-7,2) and (-2,5)
Find the volume in the region between the graphs f(x)=x^2+1 and g(x)=x over the interval [0, 4] is revolved around the x axis
3452pi/15
find the derivative of tanx
sec^(2) x
f(x)= (3^(x)-2^(x))/(x^(2)-x)
ln(2)-ln(3)
Solve the integral ∫ 1/x
ln(x)
y = (x^2 + 2) / (x^4 -3x^2 + 1)
dy/dx = (-2x^5 - 8x^3 + 14x) / (x^4 -3x^2 + 1)^2
Find the volume of the enclosed region about the y axis if you have the curves y=-y^2+6 and x=-y+4
-124.407
Solve using separation of variables dy/dx= cosx/(y^(2))
y=∛(sin(x)+c)
Limit as x approaches infinity
f(x)= (3x^(3)-2x^(2)+7x-13)/(12-2x+x^(4))
0
Solve the indefinite integral ∫ sin(4x)
-¼ cos(4x)+C
Find the derivative of 5x^3 + xy^2 = 5x^3y^3
dy/dx = (15x^2y^3 - 15x^2 - y^2)/(2xy - 15x^3y^2)
Find the volume of the solid whose base is bounded by the graphs of y= x+1 and y=x^(2)-1, with the square cross section taken perpendicular to the x-axis
8.1
Find dy/dx by using implicit differentiation, 2y^(3)+4x^(2)-y= x^(6)
y’=(6x^(5)-8x)/(6y^(2)-1)
Limit as x approaches infinity
f(x)= -(x+1)(e^(1/(x+1))-1)
-1
Solve the definite integral ∫ (x^(4))(x^(2)+3) bounds: [2,3]
626.643
Find two positive numbers whose product is 750, and where the sum of one and ten times the other is a minimum. (HINT: remember what being the minimum of a function means)
50√3 and 5√3
Find the volume of the solid whose base is bounded by the circle x^(2)+y^(2)=4, with an equilateral triangle cross section taken perpendicular to the x-axis.
(32√3)/3 or 18.475
The base of a solid is bounded by y=x^(3), y=0 and x=1. Find the volume of the solid for a semicircle cross section taken perpendicular to the y-axis.
0.039 or pi/80