Find the limit as x approaches two for the following function: (x^2-4) / (x-2)
What is 4?
100
Find the derivative of (x^3+5x^2+16x+2)
What is 3x^2+10x+16?
100
When f'(x) is positive, what is the behavior of f(x)?
What is increasing?
100
Where is a function f(x) NOT going to be differentiable?
What is where there is a cusp, corner, vertical tangent, or jump discontinuity?
200
Find the limit as x approaches infinity for the following function: (3 + 4 x^5) / (7 x^5 − 3x + 7)
What is 4/7?
200
Find the derivative of (x^2+1)/(x-5)
What is (x^2-10x-1)/(x^2-10x+25)?
200
What is the definition of an inflection point?
What is where the second derivative changes sign? (goes from concave upward to concave downward or vice versa)
200
Find the equation of the tangent line of the following function at the given point: F(x)= 4x^2-4x+1, x=1.
What is y-1=4(x-1)?
300
Find the limit as x approaches 2+ for the following function:
f(x) = (x^2+3 , x<2)
(3x+2 , x≥2)
What is 8?
300
Find the derivative of (x^3+4x^2-1)^9
What is 9(3x^2+8x)(x^3+4x^2-1)^8?
300
On what interval is a function, f(x), decreasing, given the function f'(x)= x^2+5x+2? (Calculator Allowed)
What is -4.56≤x≤-0.438?
300
What is the horizontal asymptote of the graph of y=e^x?
What is y=0?
400
Find the limit as x approaches infinity for the following function: (3+x) / (x^4-3x+7)
What is 0?
400
Find the derivative of sin(x)^2
What is 2sin(x)cos(x)?
400
What would you need from f'(x) to determine where f(x) is decreasing and concave up?
What is where f'(x) is negative and increasing?
400
The velocity, in ft/sec, of a particle moving along the x-axis is given by the function v(t)=e^t+te^t. What is the average velocity of the particle from time t=0 to time t=3?
What is 26.447 ft/sec?
500
Find the limit as h approaches o for the following function: (sin( x+h )-sin (x)) / (h)
What is sin(x)?
500
Find the derivative of ($)^4*($)^3
What is 7($)^6?
500
Let f be the function given by f'(x)=cos(x^2+1). How many relative extrema does f have on the interval 3≤x≤5? (Calculator allowed)
What is 5?
500
The radius of a circle is increasing at a constant rate of 0.2 meters per second. What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 20pi meters?