Barrons AP Calculus
BC ONLY Parametric equations were defined in Chapter One. If x = f(t) and y = g(t) are differentiable functions ...
Parametric differentiation Example 24 __ If x = 2 sin θ and y = cos 2θ, find and . SOLUTION: Also, ...
(a) (b) (a) (b) BC ONLY Example 25 __ Find the equation of the tangent to the curve in Example 24 for . SOLUTION: ...
Figure N3–7 We’ve inserted arrows to indicate the direction of motion. Note that if your calculator ca ...
Note that the derivative above holds for every point on the circle, and exists for all y different from ...
Then where we substituted for from (1) in (2), then used the given equation to simplify in (3) ...
H. DERIVATIVE OF THE INVERSE OF A FUNCTION Suppose f and g are inverse functions. What is the relationship be ...
Derivative of inverse function Simply put, the derivative of the inverse of a function at a point ...
SOLUTION: To find the slope of g at the point where x = 6, we must look at the point on f where ...
Figure N3–9 We will often refer to the Mean Value Theorem by its initials, MVT. Rolle’s Theorem If, in additi ...
(1) (2) (3) The Mean Value Theorem is one of the most useful laws when properly applied. Example 36 __ You ...
(a) (b) (c) (d) Although all indeterminate forms are listed above, only the indeterminate forms are tested on bo ...
is of type and therefore equals . Example 40 __ (Example 13) is of type and thus equals , ...
SOLUTION:. BEWARE: L’Hôpital’s Rule applies only to indeterminate forms and . Trying to use it in other si ...
SOLUTION: is of type 1∞. Let y = (1 + x)1/x, so that ln y = ln (1 + x). Then , which is of type ...
Find SOLUTION: , where f(x) = . The value of the limit is x−1/2 when x = 9, or . Example 50 __ Find ...
...
CHAPTER SUMMARY In this chapter we have reviewed differentiation. We’ve defined the derivative as t ...
1. (A) (B) (C) (D) (E) 2. (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) 4. 3. PRACTICE EXERCISES Part A. Directions: Answer these ...
(A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) (A) (B) (C) −30(5x + 1)−^4 y ...
«
4
5
6
7
8
9
10
11
12
13
»
Free download pdf