Math1011_Week09 - Math1011 Section 3.7 Consider the curve...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Math1011 Section 3.7 10/18/2010 22 Consider the curve x y - 6y + 2 = 0 Find the equation of the tangent line to the curve at point (2,1) 23 Given 5 tan re θ θθ =+ + dr d Find d dr Find
Background image of page 1

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

View Full DocumentRight Arrow Icon
Math1011 Section 3.7 1 22 Consider the curve x y - 6y + 2 = 0 Find the equation of the tangent line to the curve at point (2,1) 2 2 2 2 dd d d dx dx dx dx 2 26 2(2)(1) 44 86 2 (2) 2(1) 6 Implicit Differentiation (x y ) (6 ) (2) (0) () 6 ' 00 2' 2 6 ' 0 6 ' 2 '( 2 6) 2 ' at point (2, 1), y'= 2 dx xy y yx yyx x yy −− −+ = +− + = = −= = == = 11 12 (2 ) equation of the line tangent to the curve at (2, 1) is 1 2( 2) mx x =− 23 Given 5 tan re θ θθ =+ + dr d Find d dr Find 5t a n 10 sec 3 10 sec 3 d dr e + + + 1 10 sec 3 a n 0 s e c 3 1( 1 0 s e c 3 ) ++ + + + = (Doc #1011w.37.01)
Background image of page 2
Math1011 Section 3.8 2 -1 2 Find (f )'(3) if f(x) = x 8+x 2 1 d 1 dx 1 Show that (tan ) x + =
Background image of page 3

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

View Full DocumentRight Arrow Icon
Math1011 Section 3.8 2 -1 2 Find (f )'(3) if f(x) = x 8+x 1 1 1 '( ( )) -1 2 1/2 2 1 2 21 / 2 2 10 11 23 3 -1 3 1 10 10/3 () ' ( ) (3) 1 and '( ) ( )(8 ) (2 ) 8 '(1) (1)( )(8 (1) ) (2)(1) 8 (1) 3 (f )'(3) ff x fx ff x f = == + + + =+ + + = + = -1 Since (1) 3 implies that 1 2 1 d 1 dx 1 Show that (tan ) + = 1 2 22 2 2 1 1 '( ( )) 1 1 sec (tan ( )) 1 1 sec ( ) 1 1 (1 ) / 1 1 1 1 () t a n '( ) sec ' ( ) (tan ) (tan ) (tan ) (tan ) d dx θ + + = = = = = = = θ x²+1 x 1 (Doc #1011w.38.01)(Adams 3.1.30)
Background image of page 4
Math1011 Section 3.8 3 Differentiate the functions 2 () ln ( s in) Ft t =+ 21 23 Find f'(t) if ( ) ln ft + + =
Background image of page 5

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

View Full DocumentRight Arrow Icon
Math1011 Section 3.8 3 Differentiate the functions 2 () ln ( s in) Ft t =+ 2 2 2 2 d 1 dt 2 1 sin 1 sin 2c o s sin '( ) ln( sin ) Note: (ln ) '( ) ( sin ) '( ) (2 cos ) '( ) d dt tt + + + + =⋅+ = = 21 23 Find f'(t) if ( ) ln ft + + = 1/2 1 2 1 2 11 1 221 1 1 1 1 () ( ( ) ) ( ) (ln(2 1) ln(2 3)) '( ) (ln(2 1) ln(2 3)) '( ) [ 1) 3)] '( ) [ (2) (2)] '( ) [ ] dd + + + + ++ = = + + =− = + (Doc #1011w.38.02)
Background image of page 6
Math1011 Section 3.8 4 sin Find the derivative of x y = (x+2) Find the derivative of y=(x+1)
Background image of page 7

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

View Full DocumentRight Arrow Icon
Math1011 Section 3.8 4 sin Find the derivative of x y = sin 1 1 11 ln ln ln sin ln move exponent down ' (sin ln ) product rule y' [sin (ln ) ln (sin )] '[ s i n( )l d dx dd yx xx = = = =+ 1 sin 1 c o s) ] ' [ s i c o ] ' [ s i c o ] yy (x+2) Find the derivative of y=(x+1) (x+2) d 1 y dx 1 y dx dx y x+1 x+2 x+1 (x+2) x+2 x+1 lny =ln (x+1) y = (x+2)ln (x+1) y' = [(x+2)ln (x+1)] y' = [( 2) ln (x+1)+ln(x+1) ( 2)] y' = [( 2)( )+ln(x+1)] y' = y[ +ln(x+1)] y' = (x+1) [ +ln(x+1)] ++ + (Doc #1011w.38.03)
Background image of page 8
Math1011 Section 3.11 5 3 Find the linearization of ( ) at -8 and use this to find the value of L(-7.9) fx x a = = Find the linearization of ( ) sin( ) at 0 and use this to find the value of L(0.1) = =
Background image of page 9

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

View Full DocumentRight Arrow Icon
Math1011 Section 3.11 5 3 3
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/06/2010 for the course MATH 1110 taught by Professor Martin,c. during the Fall '06 term at Cornell University (Engineering School).

Page1 / 22

Math1011_Week09 - Math1011 Section 3.7 Consider the curve...

This preview shows document pages 1 - 11. Sign up to view the full document.

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