espwksht5 - ESP Kouba Worksheet 5 L Determine the following...

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Unformatted text preview: ESP Kouba Worksheet 5 L Determine the following limits. a. lim lxl X90 X b. lim X‘G'i Xai x-1 . 1 + sinx 0. lm — X—v +00 X2 d. lim “’0 1— x2+1 -1/x2 Let f(x) = 9 0 for x¢0 for x=0 a. Determine the following limits. 3. lim f(x) Xq-Fm ii. lim f(x) X-fi-OO iii. Iim X-9 0 f(x) b. Sketch the graph off . 3. State and explain why and where (what x-values) the following functions are continuous. a. [(x) : x 3 + sin x D. f(x) : 2 x cos x c. f(x)= 3X5 d. gztanx x2-4x e_ g: 3 {V g(x):sec2x l+cosx g. h(x):(5+cosx)5 n, h(x):[(4x3—i)20+2]'0' x—l forxg2 i. f(x): 2x2 for0<x<2 X forx<0 x-l ‘l . Determine all values of c guaranteed by the Intermediate-Value Theorem for each of the following functions f , intervals [a, b] , and values ‘rn. Illustrate each with a graph. a. f(x) = x5+1 on [4,2], m=3 b. f(x) :=3-x2 on [-2,4], m=-1 0. f(x) = m on [3.11], m=2.3 d. f(x) = :21 on [1.1.4], m=19 9. f(x) = 2 sin3x on [0.33], m=1 f. f(x)=1-e‘2X on [~ln10,0], m=-1r 2x-6 g. f(x)= on [0,1], m=-2 x2+1 x2 forx_<_1 h< f(x)= 2_)( for x>1 on [-1.2], m=1l2 ...
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espwksht5 - ESP Kouba Worksheet 5 L Determine the following...

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