2Asample_final_1 - Math 2A Sample Final Exam This exam...

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Math 2A : Sample Final Exam This exam consists of 10 questions worth 5 points each and 5 questions worth 10 points each. Read directions for each problem carefully. Please show all work needed to arrive at your solutions. Label all graphs. Clearly indicate your final answers. 1.) For what value of ? is the function ? ? = ? 2 ? < 3 2 ?? ? ≥ 3 continuous at every ? ? 2.) The theory of relativity predicts that an object whose mass is 𝑚 0 when it is at rest will appear heavier when it is moving at speeds near the speed of light. When the object is moving at speed 𝑣 , its mass 𝑚 is given by 𝑚 = 𝑚 0 1 𝑣 2 ? 2 where ? is the speed of light. Find ?𝑚 ?𝑣 and explain in terms of physics what this quantity tells you.
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3.) Show that the equation 3 ? + 2 cos ? + 5 = 0 has exactly one real root. 4.) A hyperbola is given by the equation ? 2 + 2 ?? − ? 2 + ? = 2 . Use implicit differentiation to find an equation of the tangent line to this curve at the point (1,2) .
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5.) Little Susie is enjoying a nice spherical lollipop. She sucks the lollipop in such a way that the
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