In Algebra 2 students learn about linear, quadratic, exponential, logarithmic and trigonometric functions, yet the concept of continuity is not covered. Continuity is a fundamental topic taught in most calculus courses. The purpose of this study was to explore how students understand continuity and ...
Calculus AB is designed to be the equivalent of a first-semester college calculus course. Therefore, it covers fundamental topics in calculus such as limits and continuity, differentiation, integration and accumulation of change, and differential equations. Some students elect to take Calculus AB and ...
The pair of x(t) and y(t) equations are the required parametric equations that describe the path of the baseball in calculus. Tips: If the initial velocity is known with the unit of miles per hour (mph), it can be converted to the required unit of feet per second (fps) unit. 5280...
Use the calculator to find values of y for values of x. If the calculator tells you the values or undefined, or that the values might be reaching a limit (a number that a function approaches, but never reaches), that should help you determine the range. Definition of a Range (...
I need to calculate a time derivative for a dependant variable that we use in a coupling for another physics Let's say C is the dependant variable concentration inside the rotating cylinder. I want to determine the TIME MATERIAL DERIVATIVE : d(C,TIME) (and not d(C,t) ) ...
1c was struggling to make conclusions about the original function by interpreting the graph of the derivative, specifically how to determine when the function was increasing or decreasing and how this related to concavity, Ida shared how she would respond. She began by posing a probing question,...
The function is undefined atx=3x=3, so there is a discontinuity at this point. To determine the type, we will need to evaluate the limit asxxapproaches 3. Step 2 Since the function has a0000form atx=3x=3, we need to find and divide out the common factors in the numerator and denomi...
Use the given information to determine if, at x = 2, the function is (a) continuous (b) differentiable lim_{x to 2^-} f(x) = 0, lim_{x to 2^+} f(x) = -2 If f + g is differentiable at x, are f and g necessarily differentiable at x? Give a proof or counterexample. ...
But what happens if we can’t determine what the y-value is approaching? If f(x) doesn’t approach a specific finite value as x approaches a from both directions, then we say that thelimit does not exist. Let’s look at an example of how to solve a limit graphically by investigating...
Consider the function f(x, y) = \frac{1}{x}e^{xy}. I. Compute f_x(x, y) and f_y(x, y). II. State Clariant's Theorem. To verify Clariant's Theorem (and to demonstrate its utility): III. Compute How to determine if a complex function is differentiable, given its real and...