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[DOC File]AP Calculus BC
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Parametric Equations and their Derivatives: (page 26, 144) Teach what parametric equations are and why they are useful/important. Students should be able to graph a basic parametric equation on their calculators. Include the proof for the parametric derivative in your lesson.
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Derivatives of Parametric Functions - Math24
Find the equation of the tangent line at t=3 . and find the points where the tangent is horizontal. d 2 y dx 2 = x ' t y '' t - y ' t x''(t) x'(t) 3 . The Second Derivative: of a parametric equation. Example Two: Find . d 2 y dx 2 , given x=8t+9 , y=1-4t , and . t=-3
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[DOC File]CALCULUS BC
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Experiment with other values of coefficients and of constants in the parametric equations until you can see what effect these have on the slope and y intercept of the equation in x and y. Activity. To investigate the advantage of the time parameter in parametric mode, enter the following problem. Adjust your window appropriately.
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Parametric Equations
The equations are Parametric Equations for the curve. A physical example of parametric equations is and etch-a-sketch. Think of how an etch-a-sketch works. One knob is the parametric equation for the x direction, the other knob is the parametric equation for the y direction. To move the sketcher you must independently rotate (t) the knobs.
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[DOCX File]The Derivative of the Natural Logarithmic Function
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the parametric equations x = t3 – 3t2 and y = 2t3 – 3t2 – 12t. For what values of t is the particle at rest? (A) -1 only (B) 0 only (C) 2 only (D) -1 and 2 only (E) -1, 0, and 2. 17. A curve C is defined by the parametric equations . x = t2 – 4t + 1 and y = t3. Which of the following is . an equation of the line tangent to the graph of C at
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[DOCX File]HILLGROVE
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6. A curve C is defined by the parametric equations. (a) Find in terms of t. (b) Find an equation of the tangent line to C at the point where t = 2. 7. A curve C is defined by the parametric equations. (a) Find in terms of t. (b) Find an equation of the tangent line to C at the point where t =.
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[DOC File]A.P. Calculus Formulas
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The equation of the tangent plane is given as follows:. Recall, to write the equation of a line in 3D space, we need a point and a parallel vector. Since is a vector normal to the surface, it would be parallel to any line normal to the surface at . Thus, the parametric equations of the normal line are:, , We summarize these results as follows.
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[DOC File]AB CALCULUS
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(a) Differention of a function (b) Derivative of a function (c) Derivative of a function of function (d) None . 9. When both the variables are expressed in terms of a parameter (i.e. a third variable) the involved equations are called (a) Implicit equations (b) Derivative equations (c) Parametric equations (d) None
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[DOC File]Unit
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131. p533 length of curve (parametric): 132. surface area (parametric): 133. position vector (standard form): 134. p542 speed from velocity vector: speed = 135. p542 direction from velocity vector: 136. p551 polar to Cartesian: 137. trajectory equations: 138. p552 slope of polar graph: slope at . 139. slope of polar graph at origin: slope =
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[DOC File]DIFFERENTIAL CALCULUS
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Derivative Functions: Properties and their Applications. Investigate properties of derivatives (power rule, chain rule as change of scale and as patterning, no quotient rule use product rule, Sample Problem: Examine the relationship between the derivative of a function and the derivative of its inverse. ... Parametric equations of functions ...
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Derivative of parametric equation