Category Archives: Calculus I

Calculus I

Calculus – Limits Indeterminate Form

By | March 28, 2017

Limits Indeterminate Form In this tutorial students learn how to evaluate the limit of a function when direct substitution results in the indeterminate form of infinity times 0.  Rewrite the function so that a different indeterminate form is created and then L’hopital’s Rule can be applied. Virginia Standards of Learning(SOL) APC.2, APC.8

Algebra – Find the vertex of the quadratic equation

By | November 30, 2016

Find the vertex of the quadratic equation In this tutorial students learn how to find the vertex of a quadratic equation (parabola) using various methods.  Those methods include graphing with the TI 84 C, calculus, and algebra methods like completing the square. When using the calculator I could have also used the MINIMUM function. 2ND |… Read More »

Calculus – Addendum: Derivative of f(x)=9/x Find the equation of the Tangent Line at x = 3

By | November 4, 2016

Addendum: Derivative of f(x)=9/x In this tutorial the students will learn how to use the power rule to find the derivative, create the equation of the tangent line and verify the results with the TI-84 graphing calculator. Explicit Function Point of Tangency Substitute in the value of x, 3, into the function to find the… Read More »

Calculus – Addendum – Using the TI-84C to find the tangent lines of an ellipse through a specific point

By | November 3, 2016

Using the TI-84C to find the tangent lines In this tutorial students will learn how to use the TI-84C to graph and verify their work.  The students will also learn how to convert implicit functions into explicit functions and graph using the TI-84C.  The students have already found the equations of the 2 lines that… Read More »

Calculus – Addendum – Find 2 tangent lines to an ellipse that intersect at a point not on the graph

By | November 2, 2016

Addendum – Find the tangent line equations In this tutorial the students will revisit a previous tutorial where we found the equation to 2 tangent lines.  The problem is that the equations are in a more complex form.  The students will simplify the tangent line equations and verify their results using an online graphing calculator. In… Read More »

Calculus – Find the equations of both tangent lines to the graph of the ellipse that pass through the point (0,4) not on the graph.

By | November 1, 2016

Find the equations of the tangent lines problem In this tutorial the students will answer the question below using various techniques learned in calculus.  The students will use what they have learned about calculus, implicit differentiation and basic algebra. Find the equations of both tangent lines to the graph of the ellipse that pass through the… Read More »

Calculus – Implicit Differentiation – Tangent Line

By | October 31, 2016

Implicit Differentiation – Find the Tangent Line In this tutorial students will learn to use implicit differentiation to solve a tangent line problem.  The student will create the tangent line equation at the point of tangency (1,0).  The students will then use an online graphing calculator to verify their analytical results. Implicit Function Implicit Differentiation The… Read More »

Calculus – Tangent Line at a point using Implicit Differentiation

By | October 31, 2016

Implicit Differentiation In this tutorial students learn how to find the equation of the tangent line given the point of tangency. The students then verify the solution using the GRAPH, WINDOW, CALC, dy/dx and TRACE features of the TI-84C. Implicit Function Implicit Differentiation Substitute in point (2,1) to calculate the slope Tangent Line 1) If only… Read More »

Calculus – Find the Derivative at a value of x

By | October 30, 2016

Find the derivative at a value of x In this tutorial the students will learn  how to find the derivative of a function at a specific point.  The student will find the point of tangency and the derivative.  Using this information the student will then write the equation of the tangent line. Explicit Function Derivative… Read More »

Calculus – Find the Tangent line Equation at Point (-1,1)

By | October 29, 2016

Find the Tangent line Equation at Point (-1,1) In this tutorial students learn how to find the equation of the tangent line given the function and the point of tangency. The students then verify the solution using the GRAPH, WINDOW, CALC, TANGENT and TRACE features of the TI-84C. Explicit Function Point of Tangency Derivative Slope Substitute… Read More »