espwksht16 - ESP KC)wa Worksheet" W ‘1 Evaluate the...

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Unformatted text preview: ESP KC)wa Worksheet" W ‘1. Evaluate the following limits. a. lim(1+t)1/t I b. lim(1'+1/n)n f-WO' “~44” ct lim(1-i~1/n)n ‘ d. lim(1-1ln)n nay-00 I “av-{'00 e. lim(1+3/n)4“ f. lim(1+1/n2)" “9+” h-‘V‘FOO . 1H? 9. lim(1-2/n)"2 , h. llm(1+t) Vl-w-eoo {90+ lim n + 2 3n “m n n 2 W’H’c’" n n-Iy‘oo a , Q, solveforx. Assume thatyisafunction ofxand find y‘=dy/dx. a. 3X=27 a. x2+y=1 b. 3X=20 b. x2+y2=1 C. -(1+ x/12)35=200 C. Xy3+5y=x d. lnx=10 d. (x+4y)5=7 e. ln2x=anx2+1 e. xtany+sin3x=siny3 f. lnx+ln(x—3)=ln4 f. X28902y2=Y~X g. ln(2x+1)~ln(x-3)=|nx g- mt(x-sinW)=y/x 4. Determine an equation for the line tangent to the graph of y3~x2+1=0 at x=3. 5—. Determine an equation of the line normal to the graph of y 3 x Y 2 at the point (8 1/4; 2). ‘ a y=x5 b y5=x c cos(xy)=tan(x-y) d x2y+xy2=1 e lny=xlnx f y=xx g y=3x h y=xoosx3 l y=xY ] W=XY2 k y—222 l y=xxx m. y = .7'“ n. y = x arcsecx o. y = arcsianT p. y = (arccos 3/x)5 q. x = arctan y r. y = arctany 7. With each of the following functions are given numbers x 1 (the initial x~value) and x 2 (the final x-value). Compute the associated exact change in functional value, A f, and the differential of f (approximate change in functional value), d f. a. fin =x3-+x-1 i. x1=1,x2=4 fi. x1: ,x2=2 H. x1=1,x2=1J W. x1=1,x2=101 8 . Use differentials to estimate the following quantities. a. 4229 b. (250.1)5 c. sin(1r-—.O4) d. log1o(9.9) 7 . Assume that the radius of a sphere is measured with a percentage error of at most 2% . With what percentage error will the following quantities be computed ? a. diameter of the sphere b. volume of the sphere 0. surface area of the'sphere 10. Use differentials to show that \/ 4 + h m 2 + (1 /4)h for small h. 11. Use differentials to show that W a: 1/2 — (1 /48)h3 for small h. 12. Use differentials to Show that ln(1 + hz) % h2 for small h. 13. A basketball has diameter 10 inches. A coating of ice 1 inch thick covers the basketball. a.) Use differentials to estimate the volume of ice around the basketball. b.) Compute the exact volume of ice around the basketball c.) What is the percentage error of the estimate relative to the exact value ? 14. Use basic properties of logarithms and exponents to prove that o logc x r: 1021’: , where b and c are any bases. Use this fact and your calcu- b luator to compute log7 21 . ...
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This note was uploaded on 11/30/2010 for the course MAT MAT 021A taught by Professor Kouba during the Winter '09 term at UC Davis.

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espwksht16 - ESP KC)wa Worksheet" W ‘1 Evaluate the...

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