- AP Calculus (short cut to PREVIOUS year exam questions!!) Yahoo: Calculus Homework Help. Coolmath: Precalculus concept review needed for success in Calculus. Graphing Calculator (TI-83/84) Help. Definitions: Calculus - a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series.
- Calculus 1 Review 1.Use the Squeeze Theorem. 2.If examination of the function at x = a results in an expression of the form t 0, where t is a non-zero real number, the limit does not exist. 3.If lim x!a+ f(x) 6= lim x!a f(x), the limit does not exist. 4.If examination of the function at x = a results in an expression of the form 0 0 or 1 1, the.
Test your readiness for the AP Calculus exam with this quiz!
Snow is falling at a rate of r(t) = 2e –0.1t inches per hour, where t is the time in hours since the beginning of the snowfall. Which of the following expressions gives the amount of snow, in inches, that falls from time t = 0 to time t = 5 hours? AP Calculus Chapter 1 Limits Review study guide by JohnStrayer includes 48 questions covering vocabulary, terms and more. Quizlet flashcards, activities and games help you improve your grades. Copyright © 2008 Laying the Foundation, Inc., Dallas, Texas. All rights reserved. These materials may be used for face-to-face teaching with students only.
Answer 1
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.
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.
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).
Ap Calculus Semester 1 Review
To choose between (C) and (D), take a closer look at the slopes. 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
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:
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
Review 1ap Calculus Definition
That’s (C).
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