# UCSD MATH 10A - Lecture Examples (2 pages)

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## Lecture Examples

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- School:
- University of California, San Diego
- Course:
- Math 10a - Calculus I

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9 30 08 Math 10A Lecture Examples Section 3 1 Powers and polynomials Find formulas for a Example 1 Answer a Example 2 d 3 d 1 d 1 2 x b x and c x dx dx dx d 1 d 1 2 d 3 x 3x2 b x x 2 c x dx dx dx Give an equation for the tangent line to y the curve x 9 Figure A2 Answer Tangent line y 3 1 6 1 1 2 x 2 x at x 9 and draw it with y y x 3 Figure A2 Example 3 9 x Find the derivative of y 5x3 x 2 4 Answer Example 4 18 dy 15x2 2x 3 dx 8 What is f 0 x for f x 7 3 x x x 2 3 4x 3 2 Answer f 0 x 7 3 Example 5 What is the derivative of y Answer Example 6 dy dx 3 ax1 2 2 ax2 bx c for constants a b and c x 1 bx 1 2 21 cx 3 2 2 A man driving on a straight road is s 5t2 20t 40 miles from his home t hours after noon What is his car s velocity at 4 00 PM Answer Velocity at 4 00 PM 60 miles per hour Lecture notes to accompany Section 3 1 of Calculus by Hughes Hallett et al 1 Math 10A Lecture Examples 9 30 08 Example 7 Section 3 1 p 2 A precision heater is controlled by varying the current supplied to it It produces Q I 100I2 Calories of heat in one second when the current is I amperes a What is the instantaneous rate of change of Q with respect to I at I 3 b Give an equation for the tangent line to the graph Q Q I at I 3 and draw it with the curve in an IQ plane Answer Q0 3 600 Calories per ampere b Tangent line Q 900 600 I 3 Figure A7 Q Q I Q Calories 3000 2000 1000 Figure A7 1 2 3 4 5 I amperes Interactive Examples Work the following Interactive Examples on Shenk s web page http www math ucsd edu ashenk Section 2 4 Examples 1 through 4 The chapter and section numbers on Shenk s web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course

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