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Extra info for Calculus: 1,001 Practice Problems for Dummies
Recall that lim sin x 1 and that lim cos x 1 0. x 0 x 0 x x lim 200. 2 cos x 2 lim x 0 sin x 201. lim x 0 4 lim sin( x 2 ) x2 x 6 206. lim x 0 x x 2 sin x tan x Inﬁnite Limits 207–211 Find the indicated limit using the given graph. 207. sin( 5 x ) x 199. x 205. 33 cos 2 x sin x cos x lim f ( x ) 202. sin( 5 x ) lim x 0 sin( 9 x ) 203. lim 204. indd 33 x x 0 x 3 tan(7 x ) sin( 3 x ) sin 3 ( 2 x ) 0 x3 4/4/2014 10:14:50 PM 34 Part I: The Questions 210. 208. lim f ( x ) lim f ( x ) x x 3 5 211. 209.
F(x) 3x 2 303. f(x) 304. f(x) 296. 1. 1 4/4/2014 10:15:23 PM 48 Part I: The Questions 305. f(x) 306. f(x) 4x 3 7 1 x3 8x 2 x 5 x2 Finding All Points on a Graph Where Tangent Lines Have a Given Value x 307. f (x) = (x−3 + 4)(x−2 – 5x) 308. f (x) = 4x 4 – x2 + 8x + π2 309. indd 48 x 4 310–311 Find all points on the given function where the slope of the tangent line equals the indicated value. 310. Find all x values where the function f (x) = x3 – x2 – x + 1 has a horizontal tangent line. 311. Find all x values where the function f (x) = 6x3 + 5x – 2 has a tangent line with a slope equal to 6.
Remember to rationalize denominators that contain radicals. 103. 108. 8 , where sin 5 0, find sin 2 . 0 and 9 , where sin 2 0, find Given tan Given cot cos 2 . Converting Degree Measure to Radian Measure 109–112 Convert the given degree measure to radian measure. 104. 109. 135° 110. –280° 111. 36° 112. –315° 105–108 Evaluate the trig function. Remember to rationalize denominators that contain radicals. 105. 106. indd 18 Given sin Given cos 3 , where 7 2 3 , where 3 4 2 , find cot . 2 , find csc .