Math 1914. Extra Hwk III
Baby Steps to the Chain Rule!
The Derivative as a Linear Approximation.
We saw in class that if F (a) exists, then the following expression holds
F (x) = F (a) + F (a)(x a) +
Math 1914. Extra Hwk II
Derivatives Without Dierence Quotients!
Q1. Derivative as a Linear Approximation.
We saw in class that if f (a) exists, then the following expression holds
f (a + h) = f (a) +
Math 1914. Extra Hwk IV
Linear Approximations with Error
Estimates
The Derivative as a Linear Approximation.
We saw in class that if f (a) exists, then the following expression holds
f (x) = f (a) +
Sp14: MATH 1914010 Differential and Integral Calculus l Noel Brady
Friday 02/14/2014 Midterm | 50 minutes
student m: :
Instructions.
1. Attempt all questions.
2. Do not write on back of exam sheets
1
1) a) Evaluate lim
x0
Solution:
Since this is a
0
0
sin(2x)
1
sin(x)
cos(5t) dt
0
type indeterminate, we can use Lhopital to get
1
lim
x0 sin(x)
sin(2x)
cos(5 sin(2x) cos(2x)2
= 2.
x0
cos x
cos(5t)