final1_1 - Name: Final Exam for 151N x2 + x 12 . 1. (10...

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Name: Final Exam for 151N 1. (10 points) Evaluate the limit: lim x 3 x 2 + x - 12 x - 3 . 2. (10 points) Evaluate the limit: lim x →∞ ( x - x 2 - 4 x + 7).
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3. (10 points) Find the equation of the tangent line to the graph of y = 1 /x at the point (2 , 1 / 2). You should compute the slope of the tangent line using the LIMIT DEFINITION of the derivative (no partial credit for using rules from later sections). 4. (10 points) Find the derivative of the given function of x : f ( x ) = x sin x e 2 x .
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5. (10 points) Find the equation of the tangent line to the given curve at the given point using implicit di±erentiation: (1 + xy ) 3 = 8 xy ; (1 , 1).
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6. (15 points) Do ONE of the following problems ( a) or b) ): (a) A 6-foot tall man jogs away from a 15-foot tall light post at the rate of 12 feet per second. How quickly is the tip of his shadow moving when he is 30 feet away from the base of the post? (b) A 12-foot long ladder leans against a vertical wall. If the base of the ladder slides
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final1_1 - Name: Final Exam for 151N x2 + x 12 . 1. (10...

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