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calc1-exam1f08

calc1-exam1f08 - if they exist a v b a 5(l5points Find...

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Math 111 EXAM 1, September2412008 Read each problem carefully. Show all your work for each problem! Use only the methods discussed in class. No calculators! l. (20 points) Find the limit if it exists. If the limit does not exist, explain why. a)"L%ffi b)lg#= c) ly,@# o);Sffi 2. (14 points) Usethe definition of the derivative (as the limit of a difference quotient) to find the derivative of y : \tr" + L. 3. (15 points) Evaluate the following (include * oo and - oo aspossible values of a limit). If the limit does not exist, explain why. , a) lim a;lY-," '' y7lI2* Yz*5Y*6 b) ]x.ry c) lim u+oo 4. (12 points) Find the horizontal, verticaland oblique (slanQ asymptotes,
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Unformatted text preview: if they exist. a ) v : b ) a - # 5. (l5points) Find # using the product ind quotient rules as appropriate (do not simplifr). a) a: (br3 + 2r-r)G + *) b)z: ffi c)w:@*#o 6. (12 points) Find the equations of all lines having slope -1 that are tangent to y : fi. 7. (12 points) Given the tunction f (*) : #, Find the values of r atwhich /(r) is discontinuous. For each r at which there is a discontinuity define, if possible, a new function, g(r), which extends f (r) to becontinuousat r. If acontinuousextension does not exist for a discontinuity explain why. sin0-6r a) b)...
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