quiz5Bsol - Solutions to Quiz 5B...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solutions to Quiz 5B www.math.ufl.edu/˜harringt February 25, 2008 1. Find the equation of the tangent line to the curve f (x) = point (0, −1). x3 − 2 x+2 at the First we need to find f (x) to compute the slope of the tangent line. Here we will use the quotient rule. d d (x + 2) dx (x3 − 2) − (x3 − 2) dx (x + 2) f (x) = (x + 2)2 (x + 2) ∗ (3x2 ) − (x3 − 2) ∗ 1 = (x + 2)2 Next, we need to find the slope of the tangent line at (0, −1), so the slope is m = f (0) = (0 + 2) ∗ (02 ) − (03 − 2) ∗ 1 2 1 == 2 (0 + 2) 4 2 Recall that y = m ∗ x + b where b is the y -intercept. Since the function goes through (0,-1) we already know that b = −1. Thus, the line is y = 1/2x − 1. NOTE: Notice that I did not waste time in reducing or rewriting f (x). Once I found the found the derivative, I stopped and plugged in the value that I needed. Only reduce or simplify when it is asked of you or when it will make the problem easier. Second, make sure that you are careful with your signs! 1 2. Find the derivative of the function: (a) f (x) = cos(x3 ) f (x) = − sin(x3 ) ∗ d3 x = −3x2 sin(x3 ) dx (b) g (x) = x3 ex g (x) = x3 dx d e + ex x3 = x3 ex + 3x2 ex dx dx (c) h(x) = sin(e) h (x) = 0 Notice that sin(e) is just a number, so the derivative is zero. If you do not believe me, type it in your calculator! 3. Evaluate the following limit: limx→0 sin(5x) x sin(5x) sin(5x) 5 sin(5x) = lim ∗ = 5 ∗ lim =5∗1=5 x→0 x→0 x→0 x x 5 5x lim 2 ...
View Full Document

This note was uploaded on 07/10/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

Page1 / 2

quiz5Bsol - Solutions to Quiz 5B...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online