Basics
What is the broadest definition of calculus?
1. Study of change
2. Evaluating a function
3. Calculating the slope of a straight line
Study of change
One of the uses of differential calculus is describing how steeply a curve is rising or falling.
What calculus tool is used to determine this steepness?
1. Limit
2. Integral
3. Derivative
Derivative
Find dy/dx if y = ea and a is constant.
1. ea+1/a+1
2. 1
3. 0
0
What does it tell you about your curve if the derivative has a value of 0?
1. The curve is an arc
2. The curve is vertical and parallel to the Y-axis
3. The curve is horizontal and parallel to the X-axis
The curve is horizontal at that point
Limits and derivatives are two of the three tools of calculus. Which is the third tool?
1. The golden ratio
2. Integral
3. There are only two tools, not three
Integral
What is the derivative of y wrt x where y = 3x2?
1. 3x
2. 0
3. 6x
6x
Take 'y = x3 + 2x2 + 4' to be the equation of a curve. If this equation is then differentiated with respect to 'x' it would become the derivative, 'dy/dx = 3x2 + 4x'. What characteristic of the curve does this derivative represent?
1. Y-intercept
2. The curvature
3. Slope
Slope
What does the integral of a function represent?
1. The instantaneous rate of change
2. The steepness of the function
3. The area under the function bounded by two points
The area under the graph of a function bounded by a closed interval [a,b]