1. a) Use the formal definition of a limit to show lim(5 + 3x) = 2...

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  5. 1. a) Use the formal definition of a limit to show lim(5 + 3x) = 2...


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1. a) Use the formal definition of a limit to show lim(5 + 3x) = 20 x-+5 b) Provide a careful definition of one of the following: i)lim/(x) = 8 ii) lim f(x) L x->a+ a) If lim f(x) = L, find L b) If & = 1, find the largest 8 such that If(x) - L1kE whenever 0 Consider drawing a picture) 3. Find each limit. If the limit is +00, or does not exist, say so. a) lim 2-4 x+2. b) lim x²+4x+4 7-4 c) lim d) lim (2+h)-22 sin x h->0 4.a) Verify that h(x) is continuous at x = 0 if h(x) =( x2+2 if x <0 2 cos x - sin x if x >0 b) Define 3 specific functions (i.e. via a formula f(x) = with i) a removable discontinuity ii) a jump discontinuity iii) an infinite discontinuity, where the function is even. 5. a) Show that lim 2-2 doesn't exist. x->3 px-31 b) Use the Squeeze Theorem to find lim Vxsin2(2) x->0+ c) Show that - 0 has a solution. 6. Suppose a particle is traveling on a line and it's position at time t seconds is given by 5(1)=(1+1) a) Sketch a graph of its position function. b) Find a formula the average velocity of the particle from time t = 2 to time t = 2+h for some tiny increment of time h. c) Use limits to find the instantaneous velocity by letting h - 0

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