Calculus Limits - Then determine the graphical feature illustrated

Calculus Limits Questions

Find the given limits. Show all of your work. Then determine the graphical feature illustrated by the given limit.

1. (2 points) 3x2 – 17x – 28 lim 2 x+7 x – 5x – 14

At x = 7, the graph has a: Removable discontinuity (hole) Jump discontinuity Vertical asymptote Horizontal asymptote None of the above

2. (2 points) 3x2 – 17x - 28 lim x' -5x - 14

As x > , the graph has a: x-> Removable discontinuity (hole) Jump discontinuity Vertical asymptote Horizontal asymptote None of the above

3. (2 points) lim log, (cos x) -31 X-> 2

4. (2 points) lim V 4x² + x - 2x

5. (2 points) Using the Intermediate Value Theorem, show that there is at least one solution to x? = 10+Vx. Explain your answer fully including any assumptions/conditions you must make. Provide your interval in which the solution exists.