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[DOC File]AP Calculus Free-Response Questions
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180. Let l be tangent to the graph of y = x - at the point Q, as shown in the figure above. a. Find the x-coordinate of point Q. b. Write an equation for line . c. Suppose the graph of y = x - shown in the figure, where x and y are measured in feet, represents a hill. There is a 50-foot tree growing vertically at the top of the hill. Does a
derivative of inverse

[DOC File]AP Calculus Free-Response Questions
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If g-1 is the inverse function of g, write an equation for the line tangent to the graph of y = g-1(x) at x = 2. 244. A particle moves along the x-axis with position at time t given by x(t) = e-tsin t for 0 ≤ t ≤ 2π.
derivative of cos inverse

[DOC File]Unit x: Day x: Title
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y = ln x is the inverse of x = ey the same way as is the inverse of x=ay. As a consequence, . Laws of Logarithms applied to Natural Logarithms. Recall that for any real numbers a, b, x, y>0, the following LOG RULES hold: Log of a Product Rule. Log of a Quotient Rule. Log of a Power Rule. Complete the table with these rules when a=e: LN of a ...
derivative of inverse secant

[DOC File]Math 1261 Calculus I
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implicit differentiation (often with respect to time) Differentials and linear approximation (3.11) Be able to approximate the values of y = f(x) near x = a with the tangent line . Understand the geometry of differentials . Know the definition of the differentials dy and dx for the function y = f(x) near x = a.
derivative of sin inverse

[DOC File]AP Calculus Assignments: Derivative Techniques
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8. Find the equation of the line tangent to at the point where x = 2. 9. Find the equation of the line tangent to at the point where x = 1. 10. A bug travels along the x-axis. Its position as a function of time is given by (x in meters, t in seconds; it’s a very fast bug) for t ( 0. a. Find the bug’s velocity as a function of time…
derivative of inverse trigs

[DOC File]AP Calculus AB – Final Review Sheet
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Find the range of f(x) on 31. Find f ‘ (x) by definition 32. Find the derivative of inverse to f(x) at x = a 33. y is increasing proportionally to y 34. Find the line x = c that divides the area under f(x) on [a,b] into two equal areas 35. 36. 37. The rate of change of population is… 38. The line y = mx + b is tangent to f(x…
inverse tangent function

[DOC File]AP CALCULUS AB
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A) with respect to x . B) with respect to y. Example 4: Differentiate with respect to x . Example 5: Find the equation of the tangent line at the given point. at . Derivatives of Inverse Trigonometric Functions. We learned the inverse trigonometric functions last year, and now we need to learn their derivatives.
derivative of inverse tan xy

[DOC File]Section 1
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On this problem, a horizontal tangent line means that the slope of the tangent line is 0. Since the derivative gives a formula for the slope of the tangent line, we can find the point that gives a tangent line slope of 0 by taking the derivative of the function, setting it equal to 0, and solving for x. The result of this calculation is as follows:
derivative of inverse tangent x

[DOC File]Inverse Functions
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To summarize, a function has an inverse if it is one-to-one in its domain or if its derivative is either or . Example 2: Given the polynomial function show that it is invertable (has an inverse). Solution: Taking the derivative, we find that for all We conclude that is one-to-one and invertable.
derivative of inverse

Time derivative of inverse tangent y x