# Review 1ap Calculus

• Q4 Review FRQ from AP Smacmath AP CALCULUS. Test 1 Remote: Classroom (to Edulastic). Test 1 Remote: Classroom (to Edulastic) 14 MC.
• Play this game to review Calculus. Given piecewise function f(x) shown, over which interval is f continuous?

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.  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.

## Ap Calculus Semester 1 Review With Answers

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.

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.

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. 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 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

That’s (C).

## Ap Calculus Ab Semester 1 Review

For more practice questions, check out our AP Calculus Prep Plus book.

### Unit 1 - Limits and Continuity

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