m19Am2f07

# m19Am2f07 - 1(25 points Compute the requested derivatives...

This preview shows pages 1–4. Sign up to view the full content.

1. (25 points) Compute the requested derivatives of the following functions: (a) dy dx for y = cos(cosh x ) (b) dz dt for z = q t + t 2 + e 2 t (c) f 0 ( x ) for f ( x ) = tan - 1 (1 - ke x ), where k = k ( x ) is a function of x . (d) dy dt for y = λ 2 π e - ωt 2 + α 0 , where λ,ω and α 0 are constants. (e) dy dx for y = x x , where 0 x . 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2. (10 points) Find the equation of the tangent line to the curve (called astroid) given by x 2 3 + y 2 3 = 4 at the point (3 3 , - 1). Express your answer in the form y = mx + b . 3. (10 points) Show that e x x + 1 for x VERY close to 0. In other words, show that the linearization of f ( x ) = e tan x for a = 0 is given by L ( x ) = x + 1. (Extra Credit, 3 points) Give a quadratic approximation to f ( x ) for a = 0. 2
4. (10 points) (a) (7 points) Carefully state the Mean Value Theorem (MVT). (b) (3 points) The function f ( x ) = | x | on the interval [ - 1 , 1] does not satisfy the conclusion of the MVT. Explain why this does not contradict the MVT.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

m19Am2f07 - 1(25 points Compute the requested derivatives...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online