Math 1A - Fall 2004 - Borcherds - Midterm 1

# Math 1A - Fall 2004 - Borcherds - Midterm 1 - Math 1A...

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Math 1A Midterm 1. 2fi)4-S3O 2:O0pm-3:30pm - You a.re allowed 1 sheet bf notes. Calculators are not a.llowed. Each question is worth 1 mark, which will be given only for a cleal corr€ct answer and correct working. There is no partial credit for wrong answers. There are questions on both sides of the paper. 1. Find the domain of the function f (n\ : "/i=Z 2. Sketch the graph of y : lx2 - tl. 3. Find a formula for the inverse of the function y: exp(1/i). 4. Determine the infinite limit (*oo or -oo) of , . r + l Um "':':""""' -. z-o rzb - Ll 5. Evaluate the limit . . x 2 - x - 2 Um -. t + - 1 I + l 6. Find the constant c that makes / cotrtinuous for all reals, whereg(c) : x2 - 3 if. a < 4, g(a) : @ + 20 if r > 4.

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Unformatted text preview: 7. Find the numbers at which / is discontinuous, where J is defined by f (a) -- x + 1 if c < 0, f (x) = e' if 0 < c < t, f (a) : 2 - x if s > l. 8. Evaluate ,.,,., 4c2 - 3 "!i166 az - t + 10' 9. Find the equation of the tangent line to the curve g : c3 at the point where c : l. 10. Sketch the graph ofa function for which /(0) :0, /,(O) : -t, /(t) : 0, /'(1) : -1. 11. Determine for what values ofz the function /(z) : zlzl is differentiable and find a formula for //. 12. Differentiate the function A :6r-8/s. 13. Find all points on the curve y: # +3* +3:x +l where the tangent is horizontal. 14. Differentiate (r3 + i)e". 15. Differentiate e. _ )-e ' + l ' 2...
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