{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

chbe2120practiceFinalS1probs4and5

# chbe2120practiceFinalS1probs4and5 - Problem 4[10 points All...

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: Problem 4: [10 points] All the problems below come from quizzes given in class during the semester. Each question is worth 2 points with no partial credit. (a) Write down the ﬁrst four terms of y(x)=e usmg the Taylor series to ex and aboutx— 4‘30 j/Owd 3/0): 73/0”? ’j {0%ij /0) 3—7 j/xl= imﬂ: 6 W75: 5‘ :7 f0} "ﬂWJJWV‘jYU/fo ’5 ;( a (b) The Newton-Raphson method us used to ﬁnd a root of {f1(xl,x2) =xl2 +x22 +exp(x]) f2(xisx2) = x1352 +exp(—x2) As an initial estimate for a root, we will use x1: x2— — 0. State whether this estimate is a root of theequations. {(0 0>_ 0wd+€0 :€O:/ (c) What IS the gradient of f(x, y) 2—12): —-(y+2 4 —x 2( —2)2 +16 at an arbitrary value ofx andy? Vii: [jg/E1] 33;. 276’ Z): 1,; [ 46%) Z2 6-3) (d) Which method will converge faster to a root of f (x) — x + éééo'c)"; the Newton-Raphson Imethod or the bisection method? Ir/tnéa/j in?” I’S (/{Me Cid reed, WEE woe éﬂzlwis m mm! 1W9; 4’5} raw/er (mu/470\$) wjk ﬁber/(idly (e) You are solving a problem that consists of the ODE Y” (x)— xi” + exp(— Y): x +2 with initial conditions Y(0)= 3 and Y' (0)— 0 What numerical method Would you use to calculate Y (1) r’ Problem 5: [10 points] You have purchased a machine that ﬁlls bags with candy. Each bag is supposed to weigh 16 02. A random sample of6 bags gives the following weights (in 02.): 15.87, 16.02, 15.78, 15.83, 15.69, 15.81. You wish to test the hypothesis that the machine is working correctly by giving a mean ﬁll weight of 16 02. Using the sampled data, do you accept or reject this hypothesis based on a 95% conﬁdence level? _, "z 3 O/ /§‘§/ ”6‘7? 32 3 i? g + 14g",,¢,,_:_<c(3r/f 7?“ : 5‘, <5 ’3 ...
View Full Document

{[ snackBarMessage ]}