University:
University of North Dakota
Course:
Math 165 | Calculus I
Academic year:

2024
Views:

413

Pages:

1
Author:

Meadow Benjamin

Workshop #10 1. Find the equation of the line that goes through the point (1, 1) and is parallel to the line tangent to the graph of y = x3 − x2 at x = 2. x2 ex − 2xex ex 0 , the derivative is f (x) = . Find all points where the tangent line to x2 x4 the graph of y = f (x) is horizontal. 2. For the function f (x) = 3. There are two lines that go through the point where each of those lines touch the graph. 1 2 , −2 and are tangent to the graph of f (x) = x2 . Find 4. Let l denote the tangent line to y = x2 at the point P = (3, 9). Find the equation of the line through P which is perpendicular to l. (This line is called the normal line.) 5. Compute the following limits. x2 − 4 (a) lim √ x→2+ x+2 √ (b) lim x+1−2 − 2x − 3 x→3 x2 √ √ (c) lim 2 x + 1 − 4x − 1 x→∞ (d) lim x→3− x2 + 2x + 6 2x + 6