Calculus Demystified: A Self Teaching Guide

The price of the restrict lim h→0 ( 1 + h 2 is (a) e (b) e − 1 (c) 1 /e (d) e 2 (e) 1 x 2 ln x sixty seven. utilizing logarithmic differentiation, the worth of the spinoff is x e ln x (a) x e 2 x (b) ln x x 2 ln x (c) x e 2 1 x 2 ln x (d) + − 1 · x x x ln x e 2 1 (e) − − 1 x x ln x sixty eight. The by-product of f (x) = Sin−1 (x · ln x) is 1 + ln x (a) x 2 · ln2 x 1 (b) 1 − x 2 · ln2 x 328 ultimate examination ln x (c) 1 − x 2 · ln2 x 1 + ln x (d) 1 − x 2 · ln2 x 1 + ln x (e) √ 2 1 − x sixty nine. the worth of the spinoff of Tan−1 (ex · cos x) is x e (a) 1 + e 2 x cos2 x ex sin x (b) 1 + e 2 x cos2 x x e cos x (c) 1 + e 2 x cos2 x ex ( cos x − sin x) (d) 1 + cos2 x ex ( cos x − sin x) (e) 1 + e 2 x cos2 x 70. the worth of the vital log3 x dx is x (a) x ln x − + C ln three (b) x log3 x − x + C x (c) x log3 x − + C ln three x (d) x log3 x − + C three x (e) x ln x − + C three 1 2 seventy one. the worth of the essential five x · x dx is zero four (a) ln five ln five (b) 2 ln five (c) ln 2 ultimate examination 329 2 (d) ln five ln 2 (e) ln five seventy two. the worth of the quintessential x · 2 x dx is x · 2 x 2 x (a) − + C ln 2 ln2 2 x · 2 x 2 x (b) + + C ln 2 ln2 2 x · 2 x 2 x (c) − + C ln 2 ln 2 2 x (d) − 2 x + C ln 2 x 2 x (e) − + C ln 2 ln 2 seventy three. A petri dish comprises 7,000 micro organism at 10:00 a. m. and 10,000 micro organism at 1:00 p. m. what number micro organism will there be at 4:00 p. m.? (a) 700000 (b) ten thousand (c) one hundred thousand (d) ten thousand / 7 (e) one hundred thousand / 7 seventy four. There are five grams of a radioactive substance current at midday on January 1, 2005. At midday on January 1 of 2009 there are three grams current. while will there be simply 2 grams current? (a) t = five . 127, or in early February of 2010 (b) t = 7 . 712, or in mid-August of 2012 (c) t = 7 . a hundred seventy five, or in early March of 2012 (d) t = 6 . a hundred thirty five, or in early February of 2011 (e) t = 6 . 712, or in mid-August of 2011 seventy five. If $8000 is positioned in a mark downs account with 6% curiosity compounded always, then how huge is the account after ten years? (a) 13331 . forty six (b) 11067 . 35 (c) 14771 . 05 (d) 13220 . 12 (e) 14576 . ninety five 330 ultimate examination seventy six. A filthy rich uncle needs to mend an endowment for his favourite nephew. He desires the fund to pay the younger fellow $1,000,000 in money at the day of his 30th birthday. The endowment is decided up at the day of the nephew’s start and is locked in at eight% curiosity compounded continually. How a lot precept will be placed into the account to yield the required payoff? (a) 88 , 553 . 04 (b) ninety , 717 . ninety five (c) ninety two , 769 . 23 (d) ninety one , 445 . 12 (e) ninety , 551 . ninety eight √ seventy seven. The values of Sin−11 / 2 and Tan−1 three are (a) π/ four and π/ three (b) π/ three and π/ 2 (c) π/ 2 and π/ three (d) π/ 6 and π/ three (e) π/ three and π/ 6 dx seventy eight. the price of the indispensable dx is 2 four + x 1 x (a) Tan−1 + C 2 2 1 x (b) Tan−1 + C 2 four 1 x (c) Tan−1 + C four 2 1 x 2 (d) Tan−1 + C 2 2 1 (e) Tan−1 2 + C 2 x ex dx seventy nine. the worth of the imperative √ dx 2 x 1 − e (a) Cos−1 ex + C (b) Sin−1 e 2 x + C (c) Sin−1 e − x + C (d) Cos−1 e −2 x + C (e) Sin−1 ex + C ultimate examination 331 √ 2 x dx eighty.