4.1-4.3 Quiz Left, Right, Midpoint, or Trapezoid Area Approximation, Indefinite Integrals(Including Trig), Particular Solutions, Basic Definite Integrals, Problems 73 from Section 4.4, Given v(t) and an Initial Value, then Find s(2) and a(6). The Ultimate Review Packet has everything you need to do well in your AP Calculus BC class and on the AP Exam. Exclusive review videos with tips, strategies, and content. Fill-in notes with answer keys for each unit. Practice multiple choice questions and two practice AP exams.
Test your readiness for the AP Calculus exam with this quiz!
Answer 1
The concept of a limit is one of the ideas that distinguish calculus from algebra and trigonometry. In this chapter you will define and calculate limits of function values. Most of the limits we need can be found by substitution, graphical investigation, numerical approximation, algebra, or some combination of these.
A: If the graph of a function has a sharp point, the function is not differentiable at that point. This is because the slopes directly to the left and right of the point do not approach the same value.
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An absolute value function has a sharp point at its vertex. The graph off(x)=|x + 4| is a horizontal translation (to the left 4 units) of the standard absolute value function, y =|x|, which has vertex (0, 0). Thus, the vertex of fis (-4, 0), which means the function is not differentiable at x =-4. Choice (A) is correct.
Ap Calculus Ab Precalculus Review #2
Answer 2
D: The only discontinuities that are removable are holes and holes with a point above or below—this function has neither. The function has 2 jump discontinuities (gaps), at x=-2 and x= 0, but neither of these is removable.
Answer 3
D: Examine the values in the table: f(x) increases as x gets larger, which indicates that f′(x), the slope of the function, is positive. This means f′(x)> 0, so eliminate (A) and (B).
To choose between (C) and (D), take a closer look at the slopes. Learn 2 fly 3 cool math. The slope between the first pair of points is 3, and the slope between the second pair of points is also 3, so f′(x) is constant. This means f′′(x), which is the derivative of f′(x), must be 0. Choice (D) is correct
Disk cleanup for mac el capitan. Answer 4
C: To use a local linear approximation, you need to find the equation of the tangent line. You’ve been given all the information you need in the question stem; you just need to piece it all together. The point on the function is given by f(-1)= 5, which translates to the point (-1, 5). The slope of the tangent line at x=-1 is given by f'(-1)= 2, so the slope is 2. Now the point-slope form of the tangent line is:
Ap Calculus Bc Chapter 2 Review
y-5 = 2(x-(-1))
y = 5+2(x+1)
Substituting x=-0.9 into the equation of the tangent line yields:
5+2(-0.9+1) = 5+2(0.1) = 5.2
That’s (C).
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Answer Keys > Chapter 4
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