By Steven G. Krantz

* Explains easy methods to comprehend calculus in a extra intuitive model
* makes use of sensible examples and actual facts
* Covers either differential and imperative calculus

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A) 12 seconds (b) 25 / eight seconds (c) 25 / four seconds (d) eight / 25 seconds (e) eight seconds forty three. The set of antiderivates of x 2 − cos x + four x is three x (a) − sin x + 2 x 2 + C three (b) x three + cos x + x 2 + C three x (c) − sin x + x 2 + C four (d) x 2 + x + 1 + C three x (e) − cos x − 2 x 2 + C 2 ln x forty four. The indefinite imperative + x dx equals x (a) ln x 2 + ln2 x + C 2 ln2 x x (b) + + C 2 2 1 (c) ln x + + C ln x (d) x · ln x + C (e) x 2 · ln x 2 + C forty five. The indefinite quintessential 2 x cos x 2 dx equals (a) [cos x]2 + C (b) cos x 2 + C (c) sin x 2 + C (d) [sin x]2 + C (e) sin x · cos x forty six. the world among the curve y = − x four + three x 2 + four and the x-axis is (a) 20 (b) 18 ultimate examination 323 (c) 10 ninety six (d) five seventy nine (e) five forty seven. the world among the curve y = sin 2 x + 1 / 2 and the x-axis for zero ≤ x ≤ 2 π is √ π (a) 2 three − three √ π (b) −2 three + three √ π (c) 2 three + √ three (d) √3 + π (e) three − π forty eight. the realm among the curve y = x three − nine x 2 + 26 x − 24 and the x-axis is (a) three / four (b) 2 / five (c) 2 / three (d) 1 / 2 (e) 1 / three forty nine. the world among the curves y = x 2 + x + 1 and y = − x 2 − x + thirteen is 122 (a) three a hundred twenty five (b) three 111 (c) three 119 (d) three ninety seven (e) three 50. the world among the curves y = x 2 − x and y = 2 x + four is 117 (a) 6 111 (b) 6 324 ultimate examination one hundred twenty five (c) 6 119 (d) 6 121 (e) 12 five five three fifty one. If f (x) dx = 7 and f (x) dx = 2 then f (x) dx = 1 three 1 (a) four (b) five (c) 6 (d) 7 (e) three 2 fifty two. x If F (x) = ln t dt then F (x) = x (a) ( four x − 1 ) · ln x (b) x 2 − x (c) ln x 2 − ln x (d) ln (x 2 − x) 1 1 (e) − 2 x x cos 2 x − 1 fifty three. utilizing l’Hôpital’s Rule, the restrict lim equals x→0 x 2 (a) 1 (b) zero (c) −4 (d) −2 (e) four 2 x fifty four. utilizing l’Hôpital’s Rule, the restrict lim equals x→+∞ e three x (a) −1 (b) 1 (c) −∞ (d) zero (e) +∞ √ fifty five. The restrict lim x x equals x→0 (a) 1 ultimate examination 325 (b) −1 (c) zero (d) +∞ (e) 2 √ √3 fifty six. The restrict lim three x + 1 − x equals x→+∞ (a) 2 (b) 1 (c) zero (d) −2 (e) −1 four 1 fifty seven. The fallacious fundamental √ dx equals 1 x − 1 √ (a) three − 1 √ (b) 2 ( three − 1 ) √ (c) 2 ( three + 1 ) √ (d) three + 1 √ (e) three ∞ x fifty eight. The mistaken quintessential dx equals 1 1 + x four π (a) three π (b) 2 π (c) eight 2 π (d) three three π (e) four fifty nine. the world lower than the curve y = x −4, above the x-axis, and from three to +∞, is two (a) seventy nine 1 (b) seventy nine 326 ultimate examination 2 (c) ninety seven 2 (d) eighty one 1 (e) eighty one 60. the price of log2 ( 1 / sixteen ) − log3 ( 1 / 27 ) is (a) 2 (b) three (c) four (d) 1 (e) −1 log2 27 sixty one. the price of is log2 three (a) −1 (b) 2 (c) zero (d) three (e) −3 sixty two. The graph of y = ln[1 /x 2], x = zero, is (a) concave up for all x = zero (b) concave down for all x = zero (c) concave up for x < zero and concave down for x > zero (d) concave down for x < zero and concave up for x > zero (e) by no means concave up nor concave down sixty three. The graph of y = e −1 /x 2, | x| > 2, is (a) concave up (b) concave down (c) concave up for x < zero and concave down for x > zero (d) concave down for x < zero and concave up for x > zero (e) by no means concave up nor concave down d sixty four.

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