007A Sample Midterm 1

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This is a sample, and is meant to represent the material usually covered in Math 7A for the midterm. An actual test may or may not be similar.

Click on the  boxed problem numbers  to go to a solution.

 Problem 1 

Find the following limits:

(a) Find    provided that  

(b) Find  

(c) Evaluate  

 Problem 2 

Consider the following function  

(a) Find  

(b) Find  

(c) Find  

(d) Is    continuous at    Briefly explain.

 Problem 3 


(a) Use the definition of the derivative to compute  

(b) Find the equation of the tangent line to    at  

 Problem 4 

Find the derivatives of the following functions. Do not simplify.


(b)   where


 Problem 5 

To determine drug dosages, doctors estimate a person's body surface area (BSA) (in meters squared) using the formula:

where    is the height in centimeters and    is the mass in kilograms. Calculate the rate of change of BSA with respect to height for a person of a constant mass of    What is the rate at    and    Express your results in the correct units. Does the BSA increase more rapidly with respect to height at lower or higher heights?

Contributions to this page were made by Kayla Murray