MIT 18.01 Single Variable Calculus Fall 2006 Problem Set, Study notes of Mathematics

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18.01 Single Variable Calculus

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Fall 2006

Find the tangent line to y = 1 2 3

Problem 1. (10 pts.) x at x = 1

Problem 2. Find the derivative of the following functions:

2 ( )

a. (7 pts.) 1

b. (8 pts). (2 )

c. (5 pts). = g(x)

d. (5 pts.) ln(sin x)

f x

x x

cos x x

e

Problem 3. (15 pts.) Find dy dx for the function for the function^ y^ defined^ implicitly

y^4 + xy = 4 at x =3, y = l

Problem 4. (15 pts.) Draw the graph of the derivative of the function (qualitatively accurate) directly under the graph of the function.

by