{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 3rd - 2007-2008 FALL MATH 119 WEEK 3 RECITATION QUESTIONS...

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

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.

Unformatted text preview: 2007-2008 FALL MATH 119 WEEK 3 RECITATION QUESTIONS 1)Blind application of implicit diﬀerentiation to the equation x4 + y 4 = x2 y 2 leads to the formula dy dx = 2x3 −xy 2 x2 y −2y 3 Why is this result meaningless ? 2)Write an equation of the tangent line to the curve which is the graph of the equation sin(x + 2y ) = 2xcosy 1 at the origin.(Ans:y = 2 x) 3)A rocket that is launched vertically is tracked by a radar station located on the ground 3 mi from the launch site.What is the vertical speed of the rocket at the instant that its distance from the radar is 5 mi and this distance is increasing at the rate of 5000 mi/h ? (Ans:6250 mi/h) 4)Sand is being emptied from a hopper at the rate of 10 f t3 /s.The sand forms a conical pile whose height is always twice its radius.At what rate is the radius of the pile increasing when its height is 5f t ?(Ans: 54 f t/s) π 5)Show that if A,B ,and k are constants and y = Acos(kt) + Bsin(kt) then y satisﬁes the second order diﬀerential equation of simple harmonic motion d2 y dt2 + k2 y = 0 6)Find y = d2 y dx2 if y = y (x) is deﬁned implicitly by the equation x2 − xy + y 2 = 9 d (Ans: dxy = − (2y54x)3 ) 2 − 2 7)Use a linear approximation L(x) to an appropriate function f (x),with an appropriate value of a,to estimate the number cos43◦ 1 8)(Acceleration of grawity)The acceleration a of grawity at an altitude of h miles above the surface of the earth is given by a = g ( RR h )2 + ∼ where g ∼ 32f t/s2 is the acceleration at the surface of the earth,and R = 3960 = miles is the radius of the earth.By about what percentage will a decrease if h increases from 0 to 10 miles ? (Ans:−0.5 ◦/◦ approximately ) 2 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

3rd - 2007-2008 FALL MATH 119 WEEK 3 RECITATION QUESTIONS...

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

View Full Document
Ask a homework question - tutors are online