# final - Name Final Exam for Calculus I 1 Evaluate the limit...

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Unformatted text preview: Name: Final Exam for Calculus I 1. Evaluate the limit: lim h → √ x + h- √ x h . 2. Determine where the given function is discontinuous, and justify your answer using the limit definition of continuity. f ( x ) = braceleftBigg 16 x ≤ - 4 x 2- 4 < x < 4 3 x + 5 x ≥ 4 . 3. Find all vertical and horizontal asymptotes of the given curve. y = x x 2- 4 . Sketch a graph which accurately depicts: i) any x- or y- intercepts of the curve, ii) all asymptotes of the curve, and iii) accurately suggests the correct values of the limits at the vertical asymptotes. 4. Let f ( x ) = 1 x . Find f ′ ( x ) using the definition of the derivative as a limit. 5. Find the equation of the line tangent to the curve at (1 , 1). x 3 + x 2 y + 4 y 2 = 6 . 6. If a snowball melts so that its surface area decreases at a rate of 1 square centimeter per minute, find the rate at which the diameter d decreases when d is equal 10 centimeters....
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final - Name Final Exam for Calculus I 1 Evaluate the limit...

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