Unit 1: Limits
A function can only be differentiable if it is _______ .
What is continuous?
The derivative rule that states 1/(f'(f^-1(x)) where f'(f^-1(x))ne0
What is the derivative of an inverse?
The interval that x^3-2x^2 is concave up
What is x>2/3 ?
The integral of 2x is _____.
What is x^2
When a slope field has a vertical isocline (segments are all the same along a vertical line), there is no __ in the difEQ.
What is y
The lim_(x->0)tan(x)/x
What is 1?
If f(x)=csc(x)*sin(x) , then f'(x) is
What is 0?
or
-csc(x)cot(x)sin(x)+cos(x)csc(x)
If f(3)=12 and g(x)=f^-1(x) , then g'(x) is
What is 1/10 ?
∫ ( (1 ) / (5x+2 )) dx
What is 1/5ln|5x+2| + c
Used to find the total distance traveled over an interval
What is int_a^b|v(t)| dt
Discuss the continuity of f(x) = (x-6)/(x^2 -2x -24)
What is (-infty,-4)uu(-4,6)uu(6,infty)
Find the derivative of f(x) = sinx/(x^4)
What is (xcosx - 4sinx) / (x^5) ?
A particle moves along a line so that at time t, where 0≤t≤π, its position is given by s(t) = -4cost - (t^2 /2) +10 . The velocity of the particle when its acceleration is zero is
What is (3sqrt3-pi)/3 seconds?
( sqrt3-pi/3 )
Find the particular solution to the difEQ. y' = sinx , y(π/2) = 1
What is y = -cosx + 1
Find the area of the region between y = 5x -x^2 and y = 2x
What is 4.5 (units^2)
Find lim_(x->-2)(f(x))
When x<=-2 f(x)={x^2-4x+2
When x > -2 f(x) = x^2 +4x +6
What is DNE?
Given: y= 2x^2 -6x Find: dy/dt when x=3 and dx/dt = 2
What is dy/dt = 12 ?
All edges of a cube are expanding at a rate of 3 cm/sec. The volume of the cube changing when each edge is 5 cm long is _____.
What is (dv)/dt = 225 (cm^3)/sec ?
Find f'(x) , given f(x) = int_2^(tan(x))8/t dt
What is f'(x)= (8sec^2(x))/tan(x)
The integral that finds the volume of the solid generated when the region between y = 5x - x^2 and y = 2x is rotated around the x-axis.
What is πint_0^3((5x - x^2 )^2 - (2x)^2) dx
lim_(x->infty)((6x^3-5)/(x^3+3))
Find the limit as x approaches infinity of (6x^3 -5)/(x^3 +3)
What is 6?
If x^3 + 3xy + 2y^3 = 17 , then in terms of x and y dy/dx is
What is -(x^2 + y) / (x + 2y^2) ?
f(x)= (3x-5)^2 f'(x) can be found 3 different ways. These 3 ways are
What is expand & use Power Rule, expand & use Product Rule, use the CHAIN Rule
int((x^4-4x^2-21)/(x^2-7))dx
What is x^3/3+3x+C ?
The integral that finds the volume of an object with a circular base given by (x-3)^2+(y-4)^2=1 and that has equilateral triangles perpendicular to the x-axis as cross sections
What is
sqrt3 int_2^4(1-(x-3)^2)dx